{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following additional libraries are needed to run this\n",
    "notebook. Note that running on Colab is experimental, please report a Github\n",
    "issue if you have any problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install git+https://github.com/d2l-ai/d2l-zh@release  # installing d2l\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# 概率\n",
    ":label:`sec_prob`\n",
    "\n",
    "简单地说，机器学习就是做出预测。\n",
    "\n",
    "根据病人的临床病史，我们可能想预测他们在下一年心脏病发作的*概率*。\n",
    "在飞机喷气发动机的异常检测中，我们想要评估一组发动机读数为正常运行情况的概率有多大。\n",
    "在强化学习中，我们希望智能体（agent）能在一个环境中智能地行动。\n",
    "这意味着我们需要考虑在每种可行的行为下获得高奖励的概率。\n",
    "当我们建立推荐系统时，我们也需要考虑概率。\n",
    "例如，假设我们为一家大型在线书店工作，我们可能希望估计某些用户购买特定图书的概率。\n",
    "为此，我们需要使用概率学。\n",
    "有完整的课程、专业、论文、职业、甚至院系，都致力于概率学的工作。\n",
    "所以很自然地，我们在这部分的目标不是教授你整个科目。\n",
    "相反，我们希望教给你在基础的概率知识，使你能够开始构建你的第一个深度学习模型，\n",
    "以便你可以开始自己探索它。\n",
    "\n",
    "现在让我们更认真地考虑第一个例子：根据照片区分猫和狗。\n",
    "这听起来可能很简单，但对于机器却可能是一个艰巨的挑战。\n",
    "首先，问题的难度可能取决于图像的分辨率。\n",
    "\n",
    "![不同分辨率的图像 ($10 \\times 10$, $20 \\times 20$, $40 \\times 40$, $80 \\times 80$, 和 $160 \\times 160$ pixels)](../img/cat-dog-pixels.png)\n",
    ":width:`300px`\n",
    ":label:`fig_cat_dog`\n",
    "\n",
    "如 :numref:`fig_cat_dog`所示，虽然人类很容易以$160 \\times 160$像素的分辨率识别猫和狗，\n",
    "但它在$40\\times40$像素上变得具有挑战性，而且在$10 \\times 10$像素下几乎是不可能的。\n",
    "换句话说，我们在很远的距离（从而降低分辨率）区分猫和狗的能力可能会变为猜测。\n",
    "概率给了我们一种正式的途径来说明我们的确定性水平。\n",
    "如果我们完全肯定图像是一只猫，我们说标签$y$是\"猫\"的*概率*，表示为$P(y=$\"猫\"$)$等于$1$。\n",
    "如果我们没有证据表明$y=$“猫”或$y=$“狗”，那么我们可以说这两种可能性是相等的，\n",
    "即$P(y=$\"猫\"$)=P(y=$\"狗\"$)=0.5$。\n",
    "如果我们不十分确定图像描绘的是一只猫，我们可以将概率赋值为$0.5<P(y=$\"猫\"$)<1$。\n",
    "\n",
    "现在考虑第二个例子：给出一些天气监测数据，我们想预测明天北京下雨的概率。\n",
    "如果是夏天，下雨的概率是0.5。\n",
    "\n",
    "在这两种情况下，我们都不确定结果，但这两种情况之间有一个关键区别。\n",
    "在第一种情况中，图像实际上是狗或猫二选一。\n",
    "在第二种情况下，结果实际上是一个随机的事件。\n",
    "因此，概率是一种灵活的语言，用于说明我们的确定程度，并且它可以有效地应用于广泛的领域中。\n",
    "\n",
    "## 基本概率论\n",
    "\n",
    "假设我们掷骰子，想知道看到1的几率有多大，而不是看到另一个数字。\n",
    "如果骰子是公平的，那么所有六个结果$\\{1, \\ldots, 6\\}$都有相同的可能发生，\n",
    "因此我们可以说$1$发生的概率为$\\frac{1}{6}$。\n",
    "\n",
    "然而现实生活中，对于我们从工厂收到的真实骰子，我们需要检查它是否有瑕疵。\n",
    "检查骰子的唯一方法是多次投掷并记录结果。\n",
    "对于每个骰子，我们将观察到$\\{1, \\ldots, 6\\}$中的一个值。\n",
    "对于每个值，一种自然的方法是将它出现的次数除以投掷的总次数，\n",
    "即此*事件*（event）概率的*估计值*。\n",
    "*大数定律*（law of large numbers）告诉我们：\n",
    "随着投掷次数的增加，这个估计值会越来越接近真实的潜在概率。\n",
    "让我们用代码试一试！\n",
    "\n",
    "首先，我们导入必要的软件包。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch.distributions import multinomial\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 4
   },
   "source": [
    "在统计学中，我们把从概率分布中抽取样本的过程称为*抽样*（sampling）。\n",
    "笼统来说，可以把*分布*（distribution）看作是对事件的概率分配，\n",
    "稍后我们将给出的更正式定义。\n",
    "将概率分配给一些离散选择的分布称为*多项分布*（multinomial distribution）。\n",
    "\n",
    "为了抽取一个样本，即掷骰子，我们只需传入一个概率向量。\n",
    "输出是另一个相同长度的向量：它在索引$i$处的值是采样结果中$i$出现的次数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "origin_pos": 6,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 0., 0., 0., 1.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair_probs = torch.ones([6]) / 6\n",
    "multinomial.Multinomial(1, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 8
   },
   "source": [
    "在估计一个骰子的公平性时，我们希望从同一分布中生成多个样本。\n",
    "如果用Python的for循环来完成这个任务，速度会慢得惊人。\n",
    "因此我们使用深度学习框架的函数同时抽取多个样本，得到我们想要的任意形状的独立样本数组。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "origin_pos": 10,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([3., 4., 1., 0., 1., 1.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomial.Multinomial(10, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 12
   },
   "source": [
    "现在我们知道如何对骰子进行采样，我们可以模拟1000次投掷。\n",
    "然后，我们可以统计1000次投掷后，每个数字被投中了多少次。\n",
    "具体来说，我们计算相对频率，以作为真实概率的估计。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "origin_pos": 14,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1520, 0.1820, 0.1540, 0.1760, 0.1570, 0.1790])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 将结果存储为32位浮点数以进行除法\n",
    "counts = multinomial.Multinomial(1000, fair_probs).sample()\n",
    "counts / 1000  # 相对频率作为估计值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 16
   },
   "source": [
    "因为我们是从一个公平的骰子中生成的数据，我们知道每个结果都有真实的概率$\\frac{1}{6}$，\n",
    "大约是$0.167$，所以上面输出的估计值看起来不错。\n",
    "\n",
    "我们也可以看到这些概率如何随着时间的推移收敛到真实概率。\n",
    "让我们进行500组实验，每组抽取10个样本。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "origin_pos": 18,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"289.37625pt\" version=\"1.1\" viewBox=\"0 0 392.14375 289.37625\" width=\"392.14375pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2022-01-14T02:35:21.063789</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.3, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 289.37625 \n",
       "L 392.14375 289.37625 \n",
       "L 392.14375 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 50.14375 251.82 \n",
       "L 384.94375 251.82 \n",
       "L 384.94375 7.2 \n",
       "L 50.14375 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"ma38e9d0ec5\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"65.361932\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(62.180682 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"126.356649\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 100 -->\n",
       "      <g transform=\"translate(116.812899 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"187.351365\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 200 -->\n",
       "      <g transform=\"translate(177.807615 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"248.346082\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 300 -->\n",
       "      <g transform=\"translate(238.802332 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"309.340799\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 400 -->\n",
       "      <g transform=\"translate(299.797049 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"370.335515\" xlink:href=\"#ma38e9d0ec5\" y=\"251.82\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 500 -->\n",
       "      <g transform=\"translate(360.791765 266.418437)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- Groups of experiments -->\n",
       "     <g transform=\"translate(160.397656 280.096562)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 59.515625 10.40625 \n",
       "L 59.515625 29.984375 \n",
       "L 43.40625 29.984375 \n",
       "L 43.40625 38.09375 \n",
       "L 69.28125 38.09375 \n",
       "L 69.28125 6.78125 \n",
       "Q 63.578125 2.734375 56.6875 0.65625 \n",
       "Q 49.8125 -1.421875 42 -1.421875 \n",
       "Q 24.90625 -1.421875 15.25 8.5625 \n",
       "Q 5.609375 18.5625 5.609375 36.375 \n",
       "Q 5.609375 54.25 15.25 64.234375 \n",
       "Q 24.90625 74.21875 42 74.21875 \n",
       "Q 49.125 74.21875 55.546875 72.453125 \n",
       "Q 61.96875 70.703125 67.390625 67.28125 \n",
       "L 67.390625 56.78125 \n",
       "Q 61.921875 61.421875 55.765625 63.765625 \n",
       "Q 49.609375 66.109375 42.828125 66.109375 \n",
       "Q 29.4375 66.109375 22.71875 58.640625 \n",
       "Q 16.015625 51.171875 16.015625 36.375 \n",
       "Q 16.015625 21.625 22.71875 14.15625 \n",
       "Q 29.4375 6.6875 42.828125 6.6875 \n",
       "Q 48.046875 6.6875 52.140625 7.59375 \n",
       "Q 56.25 8.5 59.515625 10.40625 \n",
       "z\n",
       "\" id=\"DejaVuSans-71\"/>\n",
       "       <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "       <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "       <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "       <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "       <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "       <path id=\"DejaVuSans-32\"/>\n",
       "       <path d=\"M 37.109375 75.984375 \n",
       "L 37.109375 68.5 \n",
       "L 28.515625 68.5 \n",
       "Q 23.6875 68.5 21.796875 66.546875 \n",
       "Q 19.921875 64.59375 19.921875 59.515625 \n",
       "L 19.921875 54.6875 \n",
       "L 34.71875 54.6875 \n",
       "L 34.71875 47.703125 \n",
       "L 19.921875 47.703125 \n",
       "L 19.921875 0 \n",
       "L 10.890625 0 \n",
       "L 10.890625 47.703125 \n",
       "L 2.296875 47.703125 \n",
       "L 2.296875 54.6875 \n",
       "L 10.890625 54.6875 \n",
       "L 10.890625 58.5 \n",
       "Q 10.890625 67.625 15.140625 71.796875 \n",
       "Q 19.390625 75.984375 28.609375 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-102\"/>\n",
       "       <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "       <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "       <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "       <path d=\"M 52 44.1875 \n",
       "Q 55.375 50.25 60.0625 53.125 \n",
       "Q 64.75 56 71.09375 56 \n",
       "Q 79.640625 56 84.28125 50.015625 \n",
       "Q 88.921875 44.046875 88.921875 33.015625 \n",
       "L 88.921875 0 \n",
       "L 79.890625 0 \n",
       "L 79.890625 32.71875 \n",
       "Q 79.890625 40.578125 77.09375 44.375 \n",
       "Q 74.3125 48.1875 68.609375 48.1875 \n",
       "Q 61.625 48.1875 57.5625 43.546875 \n",
       "Q 53.515625 38.921875 53.515625 30.90625 \n",
       "L 53.515625 0 \n",
       "L 44.484375 0 \n",
       "L 44.484375 32.71875 \n",
       "Q 44.484375 40.625 41.703125 44.40625 \n",
       "Q 38.921875 48.1875 33.109375 48.1875 \n",
       "Q 26.21875 48.1875 22.15625 43.53125 \n",
       "Q 18.109375 38.875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.1875 51.21875 25.484375 53.609375 \n",
       "Q 29.78125 56 35.6875 56 \n",
       "Q 41.65625 56 45.828125 52.96875 \n",
       "Q 50 49.953125 52 44.1875 \n",
       "z\n",
       "\" id=\"DejaVuSans-109\"/>\n",
       "       <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "       <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-71\"/>\n",
       "      <use x=\"77.490234\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"116.353516\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"177.535156\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"240.914062\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"304.390625\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"356.490234\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"388.277344\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"449.458984\" xlink:href=\"#DejaVuSans-102\"/>\n",
       "      <use x=\"484.664062\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"516.451172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"576.224609\" xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"635.404297\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"698.880859\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"760.404297\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"801.517578\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"829.300781\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "      <use x=\"926.712891\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"988.236328\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"1051.615234\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"1090.824219\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"md3dd151a6f\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"240.700909\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0.00 -->\n",
       "      <g transform=\"translate(20.878125 244.500128)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"212.903182\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0.05 -->\n",
       "      <g transform=\"translate(20.878125 216.702401)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"185.105455\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0.10 -->\n",
       "      <g transform=\"translate(20.878125 188.904674)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"157.307729\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0.15 -->\n",
       "      <g transform=\"translate(20.878125 161.106947)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"129.510002\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 0.20 -->\n",
       "      <g transform=\"translate(20.878125 133.30922)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"101.712275\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 0.25 -->\n",
       "      <g transform=\"translate(20.878125 105.511494)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"73.914548\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.30 -->\n",
       "      <g transform=\"translate(20.878125 77.713767)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"46.116821\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.35 -->\n",
       "      <g transform=\"translate(20.878125 49.91604)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#md3dd151a6f\" y=\"18.319094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 0.40 -->\n",
       "      <g transform=\"translate(20.878125 22.118313)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- Estimated probability -->\n",
       "     <g transform=\"translate(14.798438 183.033437)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 9.8125 72.90625 \n",
       "L 55.90625 72.90625 \n",
       "L 55.90625 64.59375 \n",
       "L 19.671875 64.59375 \n",
       "L 19.671875 43.015625 \n",
       "L 54.390625 43.015625 \n",
       "L 54.390625 34.71875 \n",
       "L 19.671875 34.71875 \n",
       "L 19.671875 8.296875 \n",
       "L 56.78125 8.296875 \n",
       "L 56.78125 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-69\"/>\n",
       "       <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "       <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "       <path d=\"M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "M 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 75.984375 \n",
       "L 18.109375 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-98\"/>\n",
       "       <path d=\"M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-108\"/>\n",
       "       <path d=\"M 32.171875 -5.078125 \n",
       "Q 28.375 -14.84375 24.75 -17.8125 \n",
       "Q 21.140625 -20.796875 15.09375 -20.796875 \n",
       "L 7.90625 -20.796875 \n",
       "L 7.90625 -13.28125 \n",
       "L 13.1875 -13.28125 \n",
       "Q 16.890625 -13.28125 18.9375 -11.515625 \n",
       "Q 21 -9.765625 23.484375 -3.21875 \n",
       "L 25.09375 0.875 \n",
       "L 2.984375 54.6875 \n",
       "L 12.5 54.6875 \n",
       "L 29.59375 11.921875 \n",
       "L 46.6875 54.6875 \n",
       "L 56.203125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-121\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-69\"/>\n",
       "      <use x=\"63.183594\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"115.283203\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"154.492188\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"182.275391\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "      <use x=\"279.6875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use x=\"340.966797\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"380.175781\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"441.699219\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"505.175781\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"536.962891\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"600.439453\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"639.302734\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"700.484375\" xlink:href=\"#DejaVuSans-98\"/>\n",
       "      <use x=\"763.960938\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use x=\"825.240234\" xlink:href=\"#DejaVuSans-98\"/>\n",
       "      <use x=\"888.716797\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"916.5\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "      <use x=\"944.283203\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"972.066406\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"1011.275391\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 73.914541 \n",
       "L 65.971879 129.51 \n",
       "L 66.581826 166.573634 \n",
       "L 67.191773 185.105455 \n",
       "L 67.80172 196.224547 \n",
       "L 68.411668 194.371363 \n",
       "L 69.021615 193.047662 \n",
       "L 69.631562 185.105455 \n",
       "L 70.241509 172.75091 \n",
       "L 71.461403 164.888924 \n",
       "L 72.071351 166.573634 \n",
       "L 72.681298 163.722585 \n",
       "L 73.291245 169.221036 \n",
       "L 73.901192 166.573634 \n",
       "L 74.511139 157.307725 \n",
       "L 75.121086 155.672565 \n",
       "L 76.340981 158.770769 \n",
       "L 76.950928 157.307725 \n",
       "L 77.560875 158.631426 \n",
       "L 78.780769 156.099135 \n",
       "L 79.390717 154.99125 \n",
       "L 80.000664 149.524362 \n",
       "L 80.610611 148.754579 \n",
       "L 81.220558 150.100913 \n",
       "L 81.830505 149.365518 \n",
       "L 82.440452 150.597934 \n",
       "L 83.0504 149.895005 \n",
       "L 83.660347 145.650617 \n",
       "L 84.270294 145.146223 \n",
       "L 84.880241 146.357108 \n",
       "L 85.490188 144.226443 \n",
       "L 86.100135 140.629088 \n",
       "L 87.32003 143.03322 \n",
       "L 87.929977 145.603421 \n",
       "L 88.539924 145.190768 \n",
       "L 89.149871 147.578522 \n",
       "L 89.759819 144.425856 \n",
       "L 90.369766 145.394414 \n",
       "L 90.979713 143.732098 \n",
       "L 91.58966 144.672399 \n",
       "L 92.199607 144.335457 \n",
       "L 92.809554 145.22176 \n",
       "L 93.419502 142.521702 \n",
       "L 94.029449 143.408867 \n",
       "L 95.85929 142.591282 \n",
       "L 96.469237 144.478006 \n",
       "L 98.909026 147.37997 \n",
       "L 100.12892 144.846677 \n",
       "L 100.738868 145.529027 \n",
       "L 101.958762 145.003815 \n",
       "L 103.178656 146.276882 \n",
       "L 104.398551 145.760981 \n",
       "L 105.008498 144.672399 \n",
       "L 105.618445 144.446094 \n",
       "L 106.228392 143.408867 \n",
       "L 107.448286 143.011756 \n",
       "L 108.668181 141.092392 \n",
       "L 110.498022 142.852911 \n",
       "L 111.107969 141.214304 \n",
       "L 111.717917 140.340287 \n",
       "L 112.327864 140.914195 \n",
       "L 114.157705 140.491816 \n",
       "L 114.767652 141.035892 \n",
       "L 115.3776 142.23667 \n",
       "L 115.987547 141.423311 \n",
       "L 116.597494 141.283156 \n",
       "L 117.207441 142.439173 \n",
       "L 118.427335 142.145335 \n",
       "L 119.037283 142.628032 \n",
       "L 119.64723 143.717733 \n",
       "L 120.257177 144.172536 \n",
       "L 120.867124 144.013162 \n",
       "L 121.477071 143.259417 \n",
       "L 122.087018 143.113148 \n",
       "L 122.696966 144.140385 \n",
       "L 123.306913 144.567104 \n",
       "L 123.91686 145.558172 \n",
       "L 125.136754 145.233971 \n",
       "L 125.746701 144.520778 \n",
       "L 127.576543 145.70285 \n",
       "L 128.18649 145.547153 \n",
       "L 128.796437 144.864936 \n",
       "L 129.406384 143.671108 \n",
       "L 130.016332 143.019178 \n",
       "L 130.626279 143.408867 \n",
       "L 131.236226 142.771302 \n",
       "L 131.846173 143.661573 \n",
       "L 132.45612 144.034941 \n",
       "L 133.066067 143.90525 \n",
       "L 134.285962 144.628061 \n",
       "L 134.895909 144.013162 \n",
       "L 135.505856 143.888134 \n",
       "L 136.115803 144.715593 \n",
       "L 136.72575 145.057887 \n",
       "L 137.335698 144.460037 \n",
       "L 137.945645 144.798752 \n",
       "L 138.555592 144.672399 \n",
       "L 139.165539 145.003815 \n",
       "L 139.775486 143.973861 \n",
       "L 140.385433 144.305567 \n",
       "L 140.995381 144.1872 \n",
       "L 141.605328 144.511947 \n",
       "L 142.215275 145.269345 \n",
       "L 142.825222 145.146223 \n",
       "L 143.435169 145.886953 \n",
       "L 144.045116 146.188637 \n",
       "L 144.655064 145.636931 \n",
       "L 145.265011 146.357108 \n",
       "L 145.874958 146.648452 \n",
       "L 146.484905 146.105661 \n",
       "L 147.094852 146.394545 \n",
       "L 148.924694 146.027489 \n",
       "L 149.534641 146.308628 \n",
       "L 150.144588 146.982859 \n",
       "L 150.754535 147.253228 \n",
       "L 151.364482 147.128283 \n",
       "L 151.97443 147.782632 \n",
       "L 152.584377 148.041817 \n",
       "L 153.194324 147.530597 \n",
       "L 153.804271 147.787959 \n",
       "L 154.414218 147.663619 \n",
       "L 155.024165 147.916607 \n",
       "L 155.634113 148.539318 \n",
       "L 156.24406 148.412459 \n",
       "L 156.854007 147.919092 \n",
       "L 157.463954 148.529501 \n",
       "L 158.073901 148.041817 \n",
       "L 158.683848 148.643502 \n",
       "L 159.293796 148.878737 \n",
       "L 159.903743 148.754579 \n",
       "L 161.733584 149.44045 \n",
       "L 162.343531 148.968407 \n",
       "L 163.563426 149.414545 \n",
       "L 164.173373 149.292433 \n",
       "L 165.393267 149.726534 \n",
       "L 166.003214 148.600009 \n",
       "L 166.613162 148.152786 \n",
       "L 167.223109 148.041817 \n",
       "L 167.833056 147.603193 \n",
       "L 168.443003 147.823797 \n",
       "L 169.662897 146.964385 \n",
       "L 170.272845 147.184857 \n",
       "L 170.882792 147.722305 \n",
       "L 171.492739 147.935926 \n",
       "L 172.712633 147.727723 \n",
       "L 173.932528 148.145347 \n",
       "L 175.152422 149.16806 \n",
       "L 175.762369 148.14364 \n",
       "L 176.372316 148.041817 \n",
       "L 176.982263 147.638956 \n",
       "L 177.592211 147.841476 \n",
       "L 178.202158 147.444017 \n",
       "L 179.422052 147.844674 \n",
       "L 180.031999 147.747664 \n",
       "L 180.641946 147.359069 \n",
       "L 182.471788 148.809977 \n",
       "L 183.081735 148.71049 \n",
       "L 183.691682 148.897136 \n",
       "L 185.521524 148.603389 \n",
       "L 186.131471 147.669318 \n",
       "L 187.351365 147.488628 \n",
       "L 187.961312 147.950076 \n",
       "L 189.181207 147.769294 \n",
       "L 189.791154 148.222615 \n",
       "L 191.011048 147.504667 \n",
       "L 191.620995 147.68544 \n",
       "L 192.84089 148.571304 \n",
       "L 193.450837 148.480963 \n",
       "L 194.060784 148.653717 \n",
       "L 194.670731 148.56384 \n",
       "L 195.280678 148.215018 \n",
       "L 195.890626 147.610847 \n",
       "L 196.500573 148.041817 \n",
       "L 197.720467 148.381857 \n",
       "L 198.330414 148.803399 \n",
       "L 198.940361 148.462994 \n",
       "L 199.550309 147.874108 \n",
       "L 200.770203 147.709407 \n",
       "L 201.38015 147.37997 \n",
       "L 202.600044 147.713822 \n",
       "L 203.209992 148.123459 \n",
       "L 203.819939 148.285659 \n",
       "L 204.429886 148.203669 \n",
       "L 205.039833 148.364112 \n",
       "L 205.64978 148.041817 \n",
       "L 206.259727 148.201573 \n",
       "L 206.869675 148.121355 \n",
       "L 207.479622 147.804229 \n",
       "L 208.089569 148.199535 \n",
       "L 208.699516 147.88477 \n",
       "L 209.309463 148.276397 \n",
       "L 209.91941 148.197546 \n",
       "L 210.529358 148.351975 \n",
       "L 213.579093 147.965866 \n",
       "L 214.189041 148.117461 \n",
       "L 214.798988 148.041817 \n",
       "L 215.408935 148.191872 \n",
       "L 216.018882 148.116542 \n",
       "L 217.238776 148.857222 \n",
       "L 217.848724 149.001635 \n",
       "L 219.068618 148.40806 \n",
       "L 219.678565 148.55254 \n",
       "L 220.288512 148.477865 \n",
       "L 220.898459 148.620936 \n",
       "L 221.508407 148.546575 \n",
       "L 222.118354 148.688279 \n",
       "L 222.728301 149.043538 \n",
       "L 223.338248 148.754579 \n",
       "L 223.948195 148.893856 \n",
       "L 224.558142 148.819876 \n",
       "L 225.16809 149.169228 \n",
       "L 225.778037 149.09476 \n",
       "L 226.997931 149.365518 \n",
       "L 227.607878 149.291158 \n",
       "L 228.217825 149.009903 \n",
       "L 229.43772 149.277273 \n",
       "L 231.267561 149.060048 \n",
       "L 231.877508 148.785794 \n",
       "L 233.097403 149.048981 \n",
       "L 234.317297 148.908411 \n",
       "L 234.927244 148.639617 \n",
       "L 236.147139 147.712074 \n",
       "L 237.367033 147.976337 \n",
       "L 238.586927 147.456601 \n",
       "L 239.806822 147.33154 \n",
       "L 240.416769 147.076622 \n",
       "L 241.636663 146.955471 \n",
       "L 242.856557 147.216777 \n",
       "L 243.466505 147.535832 \n",
       "L 244.076452 147.663619 \n",
       "L 245.296346 147.54096 \n",
       "L 245.906293 147.854632 \n",
       "L 246.51624 147.79307 \n",
       "L 247.126188 147.917858 \n",
       "L 247.736135 147.856504 \n",
       "L 248.346082 147.980256 \n",
       "L 249.565976 147.858335 \n",
       "L 250.175923 147.615097 \n",
       "L 250.785871 147.738021 \n",
       "L 251.395818 147.496763 \n",
       "L 252.005765 147.438176 \n",
       "L 252.615712 147.199462 \n",
       "L 253.225659 146.782377 \n",
       "L 255.055501 146.616292 \n",
       "L 256.275395 146.861452 \n",
       "L 257.495289 147.455366 \n",
       "L 258.105237 147.398759 \n",
       "L 258.715184 147.517333 \n",
       "L 259.325131 147.809449 \n",
       "L 259.935078 147.752262 \n",
       "L 260.545025 148.041817 \n",
       "L 261.154972 147.638956 \n",
       "L 261.76492 147.58283 \n",
       "L 262.374867 147.870231 \n",
       "L 263.594761 147.416513 \n",
       "L 264.204708 147.701785 \n",
       "L 266.644497 148.153797 \n",
       "L 267.254444 148.097637 \n",
       "L 267.864391 148.208772 \n",
       "L 268.474338 147.653429 \n",
       "L 269.694233 147.876353 \n",
       "L 270.914127 148.425615 \n",
       "L 271.524074 148.205814 \n",
       "L 272.743969 148.422235 \n",
       "L 273.353916 148.692057 \n",
       "L 273.963863 148.798221 \n",
       "L 274.57381 149.065375 \n",
       "L 275.183757 149.169841 \n",
       "L 275.793704 149.113027 \n",
       "L 276.403652 148.736097 \n",
       "L 277.013599 148.840604 \n",
       "L 278.233493 148.73014 \n",
       "L 278.84344 148.833778 \n",
       "L 280.063335 148.724291 \n",
       "L 280.673282 148.512965 \n",
       "L 282.503123 148.820465 \n",
       "L 283.11307 149.077114 \n",
       "L 283.723018 149.022611 \n",
       "L 284.332965 148.813978 \n",
       "L 284.942912 148.760502 \n",
       "L 285.552859 148.553749 \n",
       "L 286.772753 149.060048 \n",
       "L 287.992648 148.345621 \n",
       "L 288.602595 148.445779 \n",
       "L 289.212542 148.696472 \n",
       "L 289.822489 148.493812 \n",
       "L 291.042384 148.691179 \n",
       "L 291.652331 148.490167 \n",
       "L 292.262278 148.141188 \n",
       "L 292.872225 148.091374 \n",
       "L 293.482172 148.338331 \n",
       "L 294.092119 148.288252 \n",
       "L 294.702067 147.943506 \n",
       "L 295.312014 147.747664 \n",
       "L 295.921961 147.992922 \n",
       "L 297.141855 148.187738 \n",
       "L 297.751802 147.993304 \n",
       "L 298.971697 148.186603 \n",
       "L 300.191591 148.665945 \n",
       "L 300.801538 148.329135 \n",
       "L 302.021433 148.518218 \n",
       "L 302.63138 148.469481 \n",
       "L 303.241327 148.705362 \n",
       "L 304.461221 148.890608 \n",
       "L 305.071168 148.841416 \n",
       "L 305.681116 148.933223 \n",
       "L 306.291063 148.884171 \n",
       "L 306.90101 149.115454 \n",
       "L 308.120904 149.295855 \n",
       "L 309.950746 148.733305 \n",
       "L 310.560693 148.823563 \n",
       "L 311.17064 149.050977 \n",
       "L 312.390534 148.680848 \n",
       "L 313.000482 148.906945 \n",
       "L 313.610429 148.859401 \n",
       "L 314.220376 149.083949 \n",
       "L 314.830323 149.036206 \n",
       "L 315.44027 148.853428 \n",
       "L 316.050217 149.07636 \n",
       "L 317.270112 149.250415 \n",
       "L 317.880059 149.202846 \n",
       "L 318.490006 149.021866 \n",
       "L 319.099953 148.708435 \n",
       "L 320.319848 148.882167 \n",
       "L 320.929795 148.836039 \n",
       "L 321.539742 149.054249 \n",
       "L 324.589478 148.172329 \n",
       "L 325.199425 148.12862 \n",
       "L 325.809372 148.215018 \n",
       "L 327.029266 147.869427 \n",
       "L 327.639214 147.568846 \n",
       "L 328.249161 147.527043 \n",
       "L 328.859108 147.742229 \n",
       "L 330.079002 147.914014 \n",
       "L 330.688949 147.871805 \n",
       "L 331.298897 147.702564 \n",
       "L 331.908844 147.661026 \n",
       "L 332.518791 147.746322 \n",
       "L 333.128738 147.704875 \n",
       "L 333.738685 147.915754 \n",
       "L 334.348632 147.496763 \n",
       "L 334.95858 147.456162 \n",
       "L 335.568527 147.666179 \n",
       "L 336.788421 147.834061 \n",
       "L 337.398368 147.79307 \n",
       "L 338.008315 148.000453 \n",
       "L 338.618263 147.835453 \n",
       "L 341.058051 148.16455 \n",
       "L 341.667998 148.123459 \n",
       "L 342.277946 148.326923 \n",
       "L 342.887893 148.285659 \n",
       "L 343.49784 147.879617 \n",
       "L 344.717734 147.799574 \n",
       "L 345.327681 147.638956 \n",
       "L 345.937629 147.840821 \n",
       "L 347.76747 148.081756 \n",
       "L 349.597312 148.676739 \n",
       "L 350.207259 148.635789 \n",
       "L 351.427153 148.79098 \n",
       "L 352.0371 148.986119 \n",
       "L 354.476889 149.290279 \n",
       "L 355.086836 149.482319 \n",
       "L 355.696783 149.557003 \n",
       "L 356.916678 149.125097 \n",
       "L 357.526625 149.200054 \n",
       "L 358.136572 148.812371 \n",
       "L 359.356466 149.07776 \n",
       "L 359.966414 149.152196 \n",
       "L 360.576361 149.111702 \n",
       "L 361.186308 149.185755 \n",
       "L 361.796255 148.917035 \n",
       "L 363.626097 148.798221 \n",
       "L 364.236044 148.872167 \n",
       "L 365.455938 148.793615 \n",
       "L 366.065885 148.979665 \n",
       "L 368.505674 148.376729 \n",
       "L 369.115621 148.338919 \n",
       "L 369.725568 148.412459 \n",
       "L 369.725568 148.412459 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_17\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 185.105455 \n",
       "L 65.971879 129.51 \n",
       "L 66.581826 148.041817 \n",
       "L 67.191773 129.51 \n",
       "L 67.80172 107.271823 \n",
       "L 68.411668 110.978183 \n",
       "L 69.021615 113.625586 \n",
       "L 69.631562 129.51 \n",
       "L 70.241509 135.687272 \n",
       "L 70.851456 129.51 \n",
       "L 72.071351 138.775908 \n",
       "L 72.681298 133.786573 \n",
       "L 73.291245 133.481104 \n",
       "L 73.901192 129.51 \n",
       "L 75.121086 129.51 \n",
       "L 75.731034 126.421364 \n",
       "L 76.340981 129.51 \n",
       "L 77.560875 129.51 \n",
       "L 78.170822 132.037064 \n",
       "L 78.780769 129.51 \n",
       "L 79.390717 131.826475 \n",
       "L 80.610611 140.201433 \n",
       "L 81.220558 139.805457 \n",
       "L 82.440452 142.929591 \n",
       "L 83.0504 142.482277 \n",
       "L 83.660347 145.650617 \n",
       "L 84.270294 145.146223 \n",
       "L 84.880241 146.357108 \n",
       "L 85.490188 144.226443 \n",
       "L 86.100135 143.805978 \n",
       "L 86.710083 144.953181 \n",
       "L 87.32003 144.535798 \n",
       "L 87.929977 147.066457 \n",
       "L 88.539924 146.616292 \n",
       "L 89.759819 148.493812 \n",
       "L 90.369766 146.718116 \n",
       "L 90.979713 146.317931 \n",
       "L 91.58966 147.199462 \n",
       "L 92.199607 149.277273 \n",
       "L 93.419502 148.436111 \n",
       "L 94.639396 149.932823 \n",
       "L 95.249343 149.524362 \n",
       "L 95.85929 148.041817 \n",
       "L 96.469237 148.754579 \n",
       "L 97.079185 148.391475 \n",
       "L 97.689132 150.100913 \n",
       "L 98.909026 149.365518 \n",
       "L 99.518973 149.992537 \n",
       "L 100.12892 148.680848 \n",
       "L 101.348815 148.041817 \n",
       "L 101.958762 148.649417 \n",
       "L 102.568709 147.444017 \n",
       "L 103.788603 146.883579 \n",
       "L 104.398551 147.471612 \n",
       "L 105.008498 148.884171 \n",
       "L 105.618445 149.424793 \n",
       "L 106.228392 147.496763 \n",
       "L 106.838339 146.430358 \n",
       "L 107.448286 147.777082 \n",
       "L 108.668181 148.813978 \n",
       "L 109.888075 148.292253 \n",
       "L 111.107969 149.261019 \n",
       "L 111.717917 150.44855 \n",
       "L 112.327864 148.041817 \n",
       "L 112.937811 147.807237 \n",
       "L 113.547758 146.188637 \n",
       "L 114.157705 143.923641 \n",
       "L 114.767652 145.103848 \n",
       "L 115.987547 146.056269 \n",
       "L 116.597494 143.899417 \n",
       "L 117.817388 142.290568 \n",
       "L 118.427335 143.408867 \n",
       "L 119.037283 143.877364 \n",
       "L 120.257177 143.561597 \n",
       "L 120.867124 142.200269 \n",
       "L 121.477071 142.661617 \n",
       "L 122.087018 143.704586 \n",
       "L 122.696966 143.555169 \n",
       "L 123.306913 144.567104 \n",
       "L 123.91686 144.411872 \n",
       "L 124.526807 145.394414 \n",
       "L 125.136754 144.110826 \n",
       "L 125.746701 144.520778 \n",
       "L 126.356649 143.821702 \n",
       "L 126.966596 144.226443 \n",
       "L 128.796437 143.805978 \n",
       "L 129.406384 144.720075 \n",
       "L 130.016332 145.097511 \n",
       "L 130.626279 144.953181 \n",
       "L 131.236226 145.321553 \n",
       "L 131.846173 144.166986 \n",
       "L 133.676015 143.777861 \n",
       "L 135.505856 141.971048 \n",
       "L 136.115803 142.814894 \n",
       "L 136.72575 142.702144 \n",
       "L 137.335698 143.058471 \n",
       "L 137.945645 142.018982 \n",
       "L 139.165539 142.725315 \n",
       "L 139.775486 143.521866 \n",
       "L 140.995381 144.1872 \n",
       "L 142.215275 143.956066 \n",
       "L 142.825222 144.277541 \n",
       "L 143.435169 144.163067 \n",
       "L 144.045116 144.478006 \n",
       "L 144.655064 145.212531 \n",
       "L 145.265011 143.830044 \n",
       "L 145.874958 142.05033 \n",
       "L 146.484905 141.956741 \n",
       "L 147.094852 141.452729 \n",
       "L 147.704799 141.364914 \n",
       "L 148.314747 140.872574 \n",
       "L 148.924694 141.595974 \n",
       "L 150.144588 140.629088 \n",
       "L 151.97443 141.562165 \n",
       "L 152.584377 141.478468 \n",
       "L 153.194324 142.162757 \n",
       "L 154.414218 141.990616 \n",
       "L 155.024165 142.657574 \n",
       "L 155.634113 142.569337 \n",
       "L 156.24406 142.852911 \n",
       "L 156.854007 143.500914 \n",
       "L 157.463954 142.311586 \n",
       "L 158.073901 142.954651 \n",
       "L 158.683848 142.145335 \n",
       "L 159.903743 141.983342 \n",
       "L 160.51369 142.612118 \n",
       "L 161.123637 142.881061 \n",
       "L 161.733584 143.496283 \n",
       "L 162.343531 143.756338 \n",
       "L 162.953479 143.667853 \n",
       "L 163.563426 143.237273 \n",
       "L 164.173373 143.494138 \n",
       "L 165.393267 142.650748 \n",
       "L 166.613162 143.159184 \n",
       "L 167.223109 143.739794 \n",
       "L 168.443003 143.572384 \n",
       "L 169.662897 144.055321 \n",
       "L 170.272845 144.613969 \n",
       "L 170.882792 144.846677 \n",
       "L 171.492739 144.759036 \n",
       "L 172.102686 144.356516 \n",
       "L 172.712633 144.586738 \n",
       "L 173.32258 145.126705 \n",
       "L 173.932528 144.418284 \n",
       "L 174.542475 144.644323 \n",
       "L 175.152422 144.560709 \n",
       "L 175.762369 144.783475 \n",
       "L 176.372316 145.307619 \n",
       "L 176.982263 144.919612 \n",
       "L 178.202158 145.351717 \n",
       "L 179.422052 145.183188 \n",
       "L 180.031999 145.394414 \n",
       "L 180.641946 145.896033 \n",
       "L 181.251894 146.101311 \n",
       "L 181.861841 146.594024 \n",
       "L 182.471788 146.793561 \n",
       "L 183.081735 146.417898 \n",
       "L 184.301629 146.245368 \n",
       "L 184.911577 145.878205 \n",
       "L 186.131471 145.713702 \n",
       "L 186.741418 145.354707 \n",
       "L 187.351365 145.275873 \n",
       "L 187.961312 144.922603 \n",
       "L 189.791154 144.697053 \n",
       "L 191.011048 145.624629 \n",
       "L 191.620995 145.547153 \n",
       "L 192.230943 145.204412 \n",
       "L 192.84089 145.394414 \n",
       "L 193.450837 145.05565 \n",
       "L 194.060784 145.244567 \n",
       "L 195.890626 146.576511 \n",
       "L 197.720467 147.106727 \n",
       "L 198.330414 146.264795 \n",
       "L 198.940361 146.69405 \n",
       "L 199.550309 146.867856 \n",
       "L 200.770203 146.712184 \n",
       "L 201.38015 146.883579 \n",
       "L 201.990097 146.806369 \n",
       "L 202.600044 146.975834 \n",
       "L 203.209992 147.388719 \n",
       "L 203.819939 147.554141 \n",
       "L 204.429886 147.960895 \n",
       "L 205.039833 147.880669 \n",
       "L 205.64978 148.282494 \n",
       "L 206.259727 148.441214 \n",
       "L 206.869675 148.837174 \n",
       "L 207.479622 148.992166 \n",
       "L 208.089569 148.436111 \n",
       "L 208.699516 147.649196 \n",
       "L 209.309463 147.338076 \n",
       "L 210.529358 147.188891 \n",
       "L 211.139305 147.578522 \n",
       "L 211.749252 147.734235 \n",
       "L 212.359199 147.429196 \n",
       "L 212.969146 147.584246 \n",
       "L 213.579093 147.965866 \n",
       "L 214.189041 147.890536 \n",
       "L 214.798988 148.267814 \n",
       "L 215.408935 148.191872 \n",
       "L 216.018882 148.340717 \n",
       "L 216.628829 148.265097 \n",
       "L 217.238776 148.634837 \n",
       "L 218.458671 148.483051 \n",
       "L 219.068618 148.627803 \n",
       "L 219.678565 148.55254 \n",
       "L 220.288512 148.913904 \n",
       "L 220.898459 148.620936 \n",
       "L 221.508407 148.546575 \n",
       "L 222.118354 148.25731 \n",
       "L 222.728301 148.184921 \n",
       "L 223.338248 148.540751 \n",
       "L 223.948195 148.680848 \n",
       "L 224.558142 148.607681 \n",
       "L 225.778037 149.305349 \n",
       "L 226.387984 149.44045 \n",
       "L 226.997931 148.947514 \n",
       "L 227.607878 148.874711 \n",
       "L 228.217825 149.217344 \n",
       "L 229.43772 149.483181 \n",
       "L 230.047667 149.409483 \n",
       "L 230.657614 149.131924 \n",
       "L 231.267561 149.060048 \n",
       "L 231.877508 149.394505 \n",
       "L 232.487456 149.322199 \n",
       "L 233.70735 148.376331 \n",
       "L 234.317297 148.50845 \n",
       "L 236.147139 148.305616 \n",
       "L 236.757086 148.041817 \n",
       "L 237.367033 147.976337 \n",
       "L 238.586927 148.627033 \n",
       "L 240.416769 149.00702 \n",
       "L 241.026716 148.939552 \n",
       "L 241.636663 148.680848 \n",
       "L 244.076452 149.176419 \n",
       "L 244.686399 149.109755 \n",
       "L 245.296346 149.231361 \n",
       "L 245.906293 149.539341 \n",
       "L 246.51624 149.285566 \n",
       "L 248.956029 149.023639 \n",
       "L 250.175923 149.261019 \n",
       "L 250.785871 149.19626 \n",
       "L 251.395818 149.495293 \n",
       "L 252.005765 149.06801 \n",
       "L 252.615712 149.185018 \n",
       "L 253.225659 149.481184 \n",
       "L 253.835606 149.237417 \n",
       "L 254.445554 149.531512 \n",
       "L 256.275395 149.871395 \n",
       "L 256.885342 149.806752 \n",
       "L 257.495289 149.390653 \n",
       "L 258.715184 149.265617 \n",
       "L 259.325131 149.377969 \n",
       "L 259.935078 149.142147 \n",
       "L 260.545025 148.734597 \n",
       "L 262.984814 148.497987 \n",
       "L 264.814655 148.832808 \n",
       "L 265.424603 148.77408 \n",
       "L 266.644497 148.321754 \n",
       "L 267.254444 148.600009 \n",
       "L 268.474338 148.818601 \n",
       "L 269.084286 148.760966 \n",
       "L 269.694233 148.538208 \n",
       "L 271.524074 148.861812 \n",
       "L 272.743969 148.748308 \n",
       "L 273.353916 148.366937 \n",
       "L 273.963863 148.474045 \n",
       "L 275.183757 148.364112 \n",
       "L 275.793704 148.148942 \n",
       "L 276.403652 148.095226 \n",
       "L 277.623546 148.625914 \n",
       "L 280.673282 148.355919 \n",
       "L 281.283229 148.45944 \n",
       "L 281.893176 148.406213 \n",
       "L 282.503123 148.041817 \n",
       "L 283.11307 148.145347 \n",
       "L 285.552859 149.16806 \n",
       "L 286.162806 149.113905 \n",
       "L 288.602595 149.506187 \n",
       "L 291.042384 148.091772 \n",
       "L 292.262278 148.588337 \n",
       "L 292.872225 148.388675 \n",
       "L 293.482172 148.634837 \n",
       "L 294.092119 148.583971 \n",
       "L 294.702067 148.680848 \n",
       "L 295.312014 148.924284 \n",
       "L 295.921961 149.019753 \n",
       "L 296.531908 149.261019 \n",
       "L 297.141855 149.209175 \n",
       "L 297.751802 149.303145 \n",
       "L 298.36175 149.251467 \n",
       "L 299.581644 148.860105 \n",
       "L 301.411485 149.140357 \n",
       "L 302.021433 149.089889 \n",
       "L 302.63138 148.61203 \n",
       "L 303.241327 148.563177 \n",
       "L 303.851274 148.372744 \n",
       "L 304.461221 148.466208 \n",
       "L 305.071168 148.276993 \n",
       "L 305.681116 148.370234 \n",
       "L 306.291063 148.182212 \n",
       "L 306.90101 147.855104 \n",
       "L 307.510957 147.809009 \n",
       "L 308.120904 148.041817 \n",
       "L 308.730851 147.995491 \n",
       "L 309.340799 148.088035 \n",
       "L 310.560693 147.995839 \n",
       "L 311.17064 147.674852 \n",
       "L 311.780587 147.767273 \n",
       "L 312.390534 147.722305 \n",
       "L 313.000482 147.40436 \n",
       "L 314.220376 147.31686 \n",
       "L 314.830323 147.137827 \n",
       "L 315.44027 147.094938 \n",
       "L 316.050217 147.322137 \n",
       "L 316.660165 147.413621 \n",
       "L 317.270112 147.101798 \n",
       "L 317.880059 146.925448 \n",
       "L 318.490006 147.150866 \n",
       "L 319.099953 147.108566 \n",
       "L 319.7099 147.332468 \n",
       "L 320.319848 147.289936 \n",
       "L 320.929795 147.37997 \n",
       "L 321.539742 147.337521 \n",
       "L 322.759636 147.778954 \n",
       "L 323.369583 147.473625 \n",
       "L 323.979531 147.431358 \n",
       "L 324.589478 147.650306 \n",
       "L 325.199425 147.738021 \n",
       "L 325.809372 147.565532 \n",
       "L 327.639214 147.826829 \n",
       "L 328.249161 147.65574 \n",
       "L 328.859108 147.100249 \n",
       "L 329.469055 147.315916 \n",
       "L 330.079002 147.402794 \n",
       "L 330.688949 147.23424 \n",
       "L 331.298897 147.448126 \n",
       "L 331.908844 147.407168 \n",
       "L 333.128738 147.578522 \n",
       "L 333.738685 147.411484 \n",
       "L 334.348632 147.496763 \n",
       "L 334.95858 147.456162 \n",
       "L 335.568527 147.54096 \n",
       "L 336.178474 147.750306 \n",
       "L 336.788421 147.834061 \n",
       "L 337.398368 148.041817 \n",
       "L 338.008315 148.000453 \n",
       "L 338.618263 148.08309 \n",
       "L 339.22821 147.794727 \n",
       "L 339.838157 147.630912 \n",
       "L 341.058051 147.55091 \n",
       "L 342.277946 147.715984 \n",
       "L 344.717734 148.526312 \n",
       "L 345.937629 148.443807 \n",
       "L 347.157523 148.60218 \n",
       "L 347.76747 148.561031 \n",
       "L 348.987365 148.240658 \n",
       "L 349.597312 148.200554 \n",
       "L 350.817206 148.595005 \n",
       "L 351.427153 148.672688 \n",
       "L 352.0371 148.632003 \n",
       "L 352.647048 148.827067 \n",
       "L 353.256995 148.786225 \n",
       "L 354.476889 148.939146 \n",
       "L 355.086836 148.781536 \n",
       "L 356.306731 148.933521 \n",
       "L 356.916678 149.125097 \n",
       "L 357.526625 149.200054 \n",
       "L 358.136572 149.043538 \n",
       "L 359.356466 149.307966 \n",
       "L 359.966414 149.152196 \n",
       "L 360.576361 149.226324 \n",
       "L 361.186308 149.185755 \n",
       "L 362.406202 149.446895 \n",
       "L 363.016149 149.292433 \n",
       "L 363.626097 149.365518 \n",
       "L 364.845991 149.171805 \n",
       "L 365.455938 149.244699 \n",
       "L 366.065885 149.092208 \n",
       "L 369.725568 149.524362 \n",
       "L 369.725568 149.524362 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_18\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 185.105455 \n",
       "L 66.581826 185.105455 \n",
       "L 67.191773 171.206592 \n",
       "L 67.80172 173.986366 \n",
       "L 68.411668 185.105455 \n",
       "L 69.021615 177.163247 \n",
       "L 69.631562 150.3583 \n",
       "L 70.241509 148.041817 \n",
       "L 71.461403 154.780662 \n",
       "L 72.071351 148.041817 \n",
       "L 72.681298 146.616292 \n",
       "L 73.291245 141.423311 \n",
       "L 73.901192 144.335457 \n",
       "L 75.121086 155.672565 \n",
       "L 75.731034 148.041817 \n",
       "L 76.340981 147.066457 \n",
       "L 76.950928 151.748185 \n",
       "L 78.170822 154.780662 \n",
       "L 79.390717 152.674775 \n",
       "L 80.000664 149.524362 \n",
       "L 80.610611 150.892866 \n",
       "L 81.220558 148.041817 \n",
       "L 81.830505 149.365518 \n",
       "L 82.440452 148.680848 \n",
       "L 83.0504 149.895005 \n",
       "L 83.660347 149.237417 \n",
       "L 84.270294 146.883579 \n",
       "L 85.490188 145.861603 \n",
       "L 86.710083 148.041817 \n",
       "L 87.32003 150.546123 \n",
       "L 87.929977 145.603421 \n",
       "L 88.539924 145.190768 \n",
       "L 89.149871 143.408867 \n",
       "L 90.369766 145.394414 \n",
       "L 90.979713 145.025014 \n",
       "L 91.58966 145.93593 \n",
       "L 92.199607 148.041817 \n",
       "L 93.419502 147.253228 \n",
       "L 94.029449 149.200054 \n",
       "L 95.249343 150.636274 \n",
       "L 95.85929 149.131924 \n",
       "L 97.689132 151.130453 \n",
       "L 98.909026 150.3583 \n",
       "L 100.12892 153.473562 \n",
       "L 100.738868 153.067396 \n",
       "L 101.348815 154.527955 \n",
       "L 101.958762 155.029226 \n",
       "L 102.568709 156.411025 \n",
       "L 103.178656 155.984024 \n",
       "L 104.398551 153.458816 \n",
       "L 106.228392 154.854989 \n",
       "L 106.838339 156.099135 \n",
       "L 107.448286 156.513511 \n",
       "L 108.058234 156.133176 \n",
       "L 108.668181 154.99125 \n",
       "L 109.278128 153.119033 \n",
       "L 111.107969 156.576207 \n",
       "L 111.717917 154.780662 \n",
       "L 112.327864 155.882201 \n",
       "L 112.937811 155.548382 \n",
       "L 113.547758 154.527955 \n",
       "L 114.157705 155.591817 \n",
       "L 115.3776 153.623692 \n",
       "L 115.987547 154.660323 \n",
       "L 117.207441 155.368355 \n",
       "L 117.817388 156.349182 \n",
       "L 118.427335 156.675959 \n",
       "L 119.037283 155.746056 \n",
       "L 119.64723 156.072277 \n",
       "L 120.257177 155.780378 \n",
       "L 121.477071 157.606625 \n",
       "L 122.087018 157.307725 \n",
       "L 123.91686 158.167452 \n",
       "L 124.526807 157.87503 \n",
       "L 125.136754 158.711652 \n",
       "L 125.746701 158.419637 \n",
       "L 126.356649 157.582957 \n",
       "L 128.18649 156.77316 \n",
       "L 129.406384 158.3567 \n",
       "L 130.626279 158.852047 \n",
       "L 131.236226 158.072803 \n",
       "L 131.846173 157.813138 \n",
       "L 132.45612 158.059018 \n",
       "L 133.066067 158.79689 \n",
       "L 133.676015 159.029714 \n",
       "L 134.285962 158.283085 \n",
       "L 134.895909 158.032889 \n",
       "L 135.505856 158.745544 \n",
       "L 136.115803 158.495662 \n",
       "L 136.72575 157.778874 \n",
       "L 137.335698 158.008508 \n",
       "L 137.945645 157.77102 \n",
       "L 138.555592 157.996927 \n",
       "L 139.165539 156.852027 \n",
       "L 139.775486 157.533723 \n",
       "L 141.605328 158.190193 \n",
       "L 142.825222 157.742066 \n",
       "L 143.435169 156.661271 \n",
       "L 144.655064 156.246746 \n",
       "L 145.874958 156.680715 \n",
       "L 146.484905 156.063057 \n",
       "L 148.314747 156.699023 \n",
       "L 149.534641 157.907679 \n",
       "L 150.144588 157.704836 \n",
       "L 150.754535 156.716288 \n",
       "L 151.364482 156.524695 \n",
       "L 151.97443 157.113341 \n",
       "L 152.584377 156.535572 \n",
       "L 153.804271 156.926934 \n",
       "L 154.414218 157.496832 \n",
       "L 155.024165 157.307725 \n",
       "L 155.634113 157.867417 \n",
       "L 156.24406 157.678368 \n",
       "L 156.854007 157.860003 \n",
       "L 157.463954 157.673488 \n",
       "L 158.683848 158.029749 \n",
       "L 159.293796 157.128385 \n",
       "L 159.903743 157.307725 \n",
       "L 161.123637 156.955855 \n",
       "L 161.733584 157.1329 \n",
       "L 162.343531 156.960254 \n",
       "L 162.953479 157.480388 \n",
       "L 163.563426 157.650913 \n",
       "L 164.173373 157.137191 \n",
       "L 164.78332 157.646722 \n",
       "L 165.393267 157.476196 \n",
       "L 166.003214 157.642637 \n",
       "L 166.613162 157.141276 \n",
       "L 167.833056 157.472211 \n",
       "L 168.443003 157.307725 \n",
       "L 169.662897 157.630956 \n",
       "L 170.272845 157.14705 \n",
       "L 170.882792 156.988214 \n",
       "L 171.492739 157.46657 \n",
       "L 172.102686 157.307725 \n",
       "L 172.712633 157.46478 \n",
       "L 173.32258 156.995396 \n",
       "L 173.932528 157.463024 \n",
       "L 174.542475 156.998867 \n",
       "L 175.152422 156.84699 \n",
       "L 175.762369 157.307725 \n",
       "L 176.372316 156.852027 \n",
       "L 176.982263 156.70343 \n",
       "L 177.592211 156.255925 \n",
       "L 178.202158 156.411025 \n",
       "L 178.812105 155.969866 \n",
       "L 179.422052 156.420569 \n",
       "L 180.641946 156.137301 \n",
       "L 181.251894 156.580043 \n",
       "L 181.861841 156.439051 \n",
       "L 182.471788 155.723406 \n",
       "L 183.081735 155.874853 \n",
       "L 183.691682 156.309865 \n",
       "L 184.301629 156.173131 \n",
       "L 186.131471 156.609295 \n",
       "L 186.741418 156.473796 \n",
       "L 187.351365 156.892836 \n",
       "L 187.961312 156.757279 \n",
       "L 188.57126 156.896928 \n",
       "L 189.791154 157.714521 \n",
       "L 190.401101 157.577613 \n",
       "L 193.450837 158.229924 \n",
       "L 194.060784 158.094459 \n",
       "L 194.670731 157.699244 \n",
       "L 195.280678 157.567523 \n",
       "L 195.890626 157.178439 \n",
       "L 197.11052 156.92343 \n",
       "L 197.720467 156.542656 \n",
       "L 198.330414 156.926934 \n",
       "L 198.940361 157.055019 \n",
       "L 199.550309 157.433507 \n",
       "L 200.160256 157.057297 \n",
       "L 200.770203 157.183079 \n",
       "L 201.38015 157.555925 \n",
       "L 201.990097 157.18418 \n",
       "L 202.600044 157.307725 \n",
       "L 203.209992 156.695444 \n",
       "L 204.429886 156.458014 \n",
       "L 205.039833 156.58257 \n",
       "L 205.64978 155.743355 \n",
       "L 206.259727 155.630281 \n",
       "L 206.869675 155.756784 \n",
       "L 208.089569 155.533404 \n",
       "L 208.699516 155.894288 \n",
       "L 209.309463 155.782962 \n",
       "L 210.529358 156.028337 \n",
       "L 211.139305 155.686193 \n",
       "L 211.749252 155.116203 \n",
       "L 212.359199 155.010395 \n",
       "L 212.969146 155.134247 \n",
       "L 213.579093 154.801372 \n",
       "L 215.408935 154.494196 \n",
       "L 216.018882 154.8418 \n",
       "L 216.628829 154.96334 \n",
       "L 217.238776 154.639148 \n",
       "L 217.848724 154.982021 \n",
       "L 218.458671 155.101557 \n",
       "L 219.678565 154.900048 \n",
       "L 220.288512 154.364438 \n",
       "L 221.508407 154.171023 \n",
       "L 222.728301 154.409895 \n",
       "L 223.338248 154.1003 \n",
       "L 223.948195 154.006081 \n",
       "L 226.387984 152.797152 \n",
       "L 228.217825 153.158814 \n",
       "L 228.827773 153.484249 \n",
       "L 231.877508 154.06128 \n",
       "L 232.487456 153.972 \n",
       "L 233.097403 153.681939 \n",
       "L 233.70735 153.996082 \n",
       "L 235.537191 153.733733 \n",
       "L 236.147139 153.845381 \n",
       "L 236.757086 154.153377 \n",
       "L 237.97698 153.588317 \n",
       "L 238.586927 153.893969 \n",
       "L 239.196874 153.614322 \n",
       "L 240.416769 153.446936 \n",
       "L 241.636663 153.665271 \n",
       "L 242.24661 153.391207 \n",
       "L 242.856557 153.309424 \n",
       "L 243.466505 153.038451 \n",
       "L 244.686399 152.878935 \n",
       "L 245.296346 152.987808 \n",
       "L 245.906293 152.908759 \n",
       "L 247.126188 153.124128 \n",
       "L 248.346082 153.70603 \n",
       "L 248.956029 153.25773 \n",
       "L 249.565976 153.546324 \n",
       "L 250.175923 153.650135 \n",
       "L 251.395818 153.492351 \n",
       "L 252.005765 153.776422 \n",
       "L 252.615712 153.878138 \n",
       "L 253.225659 153.799279 \n",
       "L 253.835606 153.541585 \n",
       "L 254.445554 153.643077 \n",
       "L 255.055501 153.565726 \n",
       "L 255.665448 153.13363 \n",
       "L 256.275395 153.412506 \n",
       "L 257.495289 153.261226 \n",
       "L 258.105237 153.361682 \n",
       "L 258.715184 153.636333 \n",
       "L 259.325131 153.734984 \n",
       "L 259.935078 153.659273 \n",
       "L 260.545025 153.757244 \n",
       "L 261.154972 154.027248 \n",
       "L 261.76492 153.951347 \n",
       "L 262.374867 153.704323 \n",
       "L 262.984814 153.629872 \n",
       "L 263.594761 153.214808 \n",
       "L 264.204708 153.14232 \n",
       "L 264.814655 152.561776 \n",
       "L 266.03455 152.422069 \n",
       "L 267.254444 151.949131 \n",
       "L 267.864391 151.547836 \n",
       "L 268.474338 151.648309 \n",
       "L 269.084286 151.416272 \n",
       "L 269.694233 151.351074 \n",
       "L 270.30418 150.956316 \n",
       "L 270.914127 151.221838 \n",
       "L 271.524074 151.321789 \n",
       "L 272.134021 151.094118 \n",
       "L 272.743969 151.356898 \n",
       "L 273.353916 151.130453 \n",
       "L 273.963863 151.229509 \n",
       "L 275.183757 151.103595 \n",
       "L 275.793704 151.201872 \n",
       "L 276.403652 151.139359 \n",
       "L 277.013599 150.597934 \n",
       "L 277.623546 150.537508 \n",
       "L 278.233493 150.318585 \n",
       "L 278.84344 150.259302 \n",
       "L 279.453387 150.3583 \n",
       "L 280.063335 150.299233 \n",
       "L 280.673282 150.39756 \n",
       "L 281.283229 150.338724 \n",
       "L 283.11307 149.698293 \n",
       "L 284.332965 149.586139 \n",
       "L 284.942912 149.684532 \n",
       "L 285.552859 149.47522 \n",
       "L 286.162806 149.42022 \n",
       "L 286.772753 149.212787 \n",
       "L 287.382701 149.158806 \n",
       "L 287.992648 149.40892 \n",
       "L 288.602595 149.354699 \n",
       "L 289.822489 149.54847 \n",
       "L 290.432436 149.494315 \n",
       "L 292.262278 149.780731 \n",
       "L 292.872225 150.023835 \n",
       "L 293.482172 149.820877 \n",
       "L 294.702067 150.302994 \n",
       "L 295.312014 150.247985 \n",
       "L 295.921961 150.046584 \n",
       "L 296.531908 150.138839 \n",
       "L 297.141855 149.93878 \n",
       "L 298.36175 150.122419 \n",
       "L 298.971697 149.923959 \n",
       "L 301.411485 149.713503 \n",
       "L 302.021433 149.80449 \n",
       "L 302.63138 150.037554 \n",
       "L 303.851274 149.932823 \n",
       "L 304.461221 149.739392 \n",
       "L 305.071168 149.829153 \n",
       "L 305.681116 149.777715 \n",
       "L 307.510957 150.463064 \n",
       "L 308.120904 150.549884 \n",
       "L 311.17064 150.28949 \n",
       "L 311.780587 150.375457 \n",
       "L 312.390534 150.597934 \n",
       "L 313.000482 150.546123 \n",
       "L 313.610429 150.767084 \n",
       "L 314.220376 150.715116 \n",
       "L 314.830323 150.798995 \n",
       "L 315.44027 151.017736 \n",
       "L 316.050217 150.425768 \n",
       "L 317.270112 150.324724 \n",
       "L 319.099953 150.574945 \n",
       "L 320.319848 150.474397 \n",
       "L 320.929795 150.556852 \n",
       "L 321.539742 150.374803 \n",
       "L 322.149689 150.457108 \n",
       "L 322.759636 150.407584 \n",
       "L 323.979531 150.570869 \n",
       "L 324.589478 150.521428 \n",
       "L 327.639214 150.92264 \n",
       "L 328.249161 150.744377 \n",
       "L 328.859108 150.823732 \n",
       "L 329.469055 150.774623 \n",
       "L 330.079002 150.597934 \n",
       "L 332.518791 150.405786 \n",
       "L 333.128738 150.231947 \n",
       "L 333.738685 150.311021 \n",
       "L 334.348632 150.515521 \n",
       "L 334.95858 150.593601 \n",
       "L 335.568527 150.295687 \n",
       "L 336.178474 150.373916 \n",
       "L 338.008315 150.2342 \n",
       "L 338.618263 150.311866 \n",
       "L 339.22821 150.512729 \n",
       "L 339.838157 150.589434 \n",
       "L 340.448104 150.419795 \n",
       "L 341.667998 150.327681 \n",
       "L 342.277946 150.037554 \n",
       "L 342.887893 150.236379 \n",
       "L 343.49784 150.191022 \n",
       "L 344.107787 150.388646 \n",
       "L 344.717734 150.222031 \n",
       "L 345.937629 150.373369 \n",
       "L 346.547576 150.328211 \n",
       "L 347.157523 150.403326 \n",
       "L 347.76747 150.597934 \n",
       "L 348.377417 150.672145 \n",
       "L 348.987365 150.865337 \n",
       "L 349.597312 150.938653 \n",
       "L 350.817206 150.017489 \n",
       "L 351.427153 149.973864 \n",
       "L 352.0371 149.694341 \n",
       "L 352.647048 149.887152 \n",
       "L 353.256995 149.961603 \n",
       "L 353.866942 149.918458 \n",
       "L 354.476889 149.758454 \n",
       "L 355.086836 149.949508 \n",
       "L 355.696783 149.906653 \n",
       "L 356.306731 149.747676 \n",
       "L 356.916678 149.705426 \n",
       "L 357.526625 149.779181 \n",
       "L 358.136572 149.968206 \n",
       "L 358.746519 149.810413 \n",
       "L 359.966414 149.95626 \n",
       "L 360.576361 150.143362 \n",
       "L 361.186308 150.100913 \n",
       "L 362.406202 149.902594 \n",
       "L 363.016149 149.86089 \n",
       "L 363.626097 149.705898 \n",
       "L 364.845991 149.849806 \n",
       "L 366.065885 149.42983 \n",
       "L 366.675832 149.164962 \n",
       "L 368.505674 149.381465 \n",
       "L 369.115621 149.341642 \n",
       "L 369.725568 149.413178 \n",
       "L 369.725568 149.413178 \n",
       "\" style=\"fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_19\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 240.700909 \n",
       "L 65.971879 212.903182 \n",
       "L 66.581826 166.573634 \n",
       "L 67.191773 143.408867 \n",
       "L 67.80172 140.629088 \n",
       "L 68.411668 138.775908 \n",
       "L 69.021615 153.336622 \n",
       "L 69.631562 157.307725 \n",
       "L 70.241509 160.396361 \n",
       "L 70.851456 162.867274 \n",
       "L 71.461403 169.94306 \n",
       "L 72.071351 171.206592 \n",
       "L 72.681298 167.999158 \n",
       "L 73.291245 173.192144 \n",
       "L 73.901192 173.986366 \n",
       "L 75.121086 162.213206 \n",
       "L 75.731034 166.573634 \n",
       "L 76.340981 164.622922 \n",
       "L 76.950928 165.647044 \n",
       "L 77.560875 161.278829 \n",
       "L 78.170822 162.361861 \n",
       "L 79.390717 168.890117 \n",
       "L 80.000664 169.538725 \n",
       "L 81.220558 166.573634 \n",
       "L 81.830505 163.264385 \n",
       "L 83.0504 164.720454 \n",
       "L 83.660347 161.791234 \n",
       "L 84.270294 164.257159 \n",
       "L 84.880241 161.519506 \n",
       "L 85.490188 162.213206 \n",
       "L 86.100135 161.278829 \n",
       "L 86.710083 155.763411 \n",
       "L 87.32003 156.556441 \n",
       "L 87.929977 158.770769 \n",
       "L 88.539924 159.446012 \n",
       "L 89.149871 157.307725 \n",
       "L 89.759819 156.629733 \n",
       "L 90.369766 157.307725 \n",
       "L 90.979713 159.247104 \n",
       "L 91.58966 157.307725 \n",
       "L 92.199607 154.219089 \n",
       "L 92.809554 152.473341 \n",
       "L 93.419502 153.167645 \n",
       "L 94.029449 152.674775 \n",
       "L 94.639396 151.067425 \n",
       "L 95.85929 154.582458 \n",
       "L 96.469237 153.031152 \n",
       "L 98.299079 151.748185 \n",
       "L 98.909026 153.336622 \n",
       "L 99.518973 151.943257 \n",
       "L 100.12892 153.473562 \n",
       "L 100.738868 153.067396 \n",
       "L 101.348815 151.748185 \n",
       "L 101.958762 149.560822 \n",
       "L 102.568709 150.134125 \n",
       "L 103.178656 149.806752 \n",
       "L 103.788603 151.226974 \n",
       "L 104.398551 150.892866 \n",
       "L 105.008498 149.726534 \n",
       "L 105.618445 149.424793 \n",
       "L 106.228392 149.949508 \n",
       "L 107.448286 149.365518 \n",
       "L 108.058234 150.651931 \n",
       "L 108.668181 150.3583 \n",
       "L 109.278128 150.834287 \n",
       "L 109.888075 149.043538 \n",
       "L 110.498022 148.783094 \n",
       "L 111.107969 149.992537 \n",
       "L 111.717917 150.44855 \n",
       "L 112.327864 151.605628 \n",
       "L 112.937811 151.325939 \n",
       "L 113.547758 152.443128 \n",
       "L 114.157705 152.846361 \n",
       "L 114.767652 151.205791 \n",
       "L 115.3776 152.284043 \n",
       "L 115.987547 151.351074 \n",
       "L 116.597494 151.748185 \n",
       "L 117.817388 151.236957 \n",
       "L 118.427335 150.3583 \n",
       "L 119.64723 149.895005 \n",
       "L 120.257177 149.060048 \n",
       "L 121.477071 148.639617 \n",
       "L 122.087018 149.027557 \n",
       "L 122.696966 149.992537 \n",
       "L 124.526807 147.663619 \n",
       "L 125.136754 148.041817 \n",
       "L 126.356649 149.876655 \n",
       "L 126.966596 149.676977 \n",
       "L 127.576543 148.941425 \n",
       "L 128.18649 149.289153 \n",
       "L 129.406384 148.915958 \n",
       "L 130.016332 149.254184 \n",
       "L 131.236226 148.891901 \n",
       "L 131.846173 149.221113 \n",
       "L 132.45612 149.043538 \n",
       "L 133.066067 149.365518 \n",
       "L 133.676015 148.205814 \n",
       "L 134.895909 148.847554 \n",
       "L 135.505856 148.201573 \n",
       "L 137.335698 147.730358 \n",
       "L 138.555592 148.348131 \n",
       "L 139.165539 148.193719 \n",
       "L 139.775486 148.945807 \n",
       "L 140.385433 148.340717 \n",
       "L 140.995381 148.190074 \n",
       "L 141.605328 147.600583 \n",
       "L 142.215275 147.458142 \n",
       "L 142.825222 148.186603 \n",
       "L 144.045116 147.899268 \n",
       "L 144.655064 148.183281 \n",
       "L 145.265011 147.62064 \n",
       "L 145.874958 147.902482 \n",
       "L 147.094852 149.277273 \n",
       "L 147.704799 149.131924 \n",
       "L 148.924694 149.653284 \n",
       "L 149.534641 149.508365 \n",
       "L 150.144588 148.968407 \n",
       "L 150.754535 149.2247 \n",
       "L 151.97443 148.948972 \n",
       "L 152.584377 149.200054 \n",
       "L 153.194324 149.064265 \n",
       "L 153.804271 148.549541 \n",
       "L 154.414218 149.176419 \n",
       "L 155.024165 149.419184 \n",
       "L 155.634113 148.539318 \n",
       "L 156.24406 148.783094 \n",
       "L 156.854007 149.391821 \n",
       "L 158.683848 149.00451 \n",
       "L 159.293796 149.596105 \n",
       "L 159.903743 149.823726 \n",
       "L 160.51369 149.340226 \n",
       "L 161.123637 149.566588 \n",
       "L 161.733584 148.391475 \n",
       "L 162.953479 148.156928 \n",
       "L 163.563426 147.698637 \n",
       "L 164.173373 148.269206 \n",
       "L 165.393267 148.7157 \n",
       "L 166.003214 149.269834 \n",
       "L 166.613162 149.484415 \n",
       "L 167.223109 149.365518 \n",
       "L 167.833056 149.577001 \n",
       "L 168.443003 149.458957 \n",
       "L 170.272845 150.077104 \n",
       "L 170.882792 149.319879 \n",
       "L 171.492739 149.206674 \n",
       "L 172.102686 149.410643 \n",
       "L 172.712633 149.926411 \n",
       "L 173.932528 150.319471 \n",
       "L 174.542475 149.586139 \n",
       "L 175.152422 149.782379 \n",
       "L 175.762369 149.670988 \n",
       "L 176.372316 148.953222 \n",
       "L 176.982263 149.149702 \n",
       "L 177.592211 149.043538 \n",
       "L 178.812105 149.429225 \n",
       "L 179.422052 149.323276 \n",
       "L 180.031999 149.512599 \n",
       "L 181.251894 149.303145 \n",
       "L 181.861841 149.779181 \n",
       "L 183.081735 150.143362 \n",
       "L 183.691682 150.037554 \n",
       "L 184.911577 150.393575 \n",
       "L 186.131471 151.301185 \n",
       "L 187.351365 151.637547 \n",
       "L 188.57126 150.871798 \n",
       "L 189.181207 151.039615 \n",
       "L 190.401101 150.830592 \n",
       "L 191.011048 151.264743 \n",
       "L 191.620995 150.892866 \n",
       "L 192.230943 151.322576 \n",
       "L 192.84089 150.953963 \n",
       "L 193.450837 151.115814 \n",
       "L 194.060784 150.489417 \n",
       "L 194.670731 150.912947 \n",
       "L 195.280678 151.072727 \n",
       "L 195.890626 151.489597 \n",
       "L 196.500573 151.130453 \n",
       "L 197.720467 150.9321 \n",
       "L 198.330414 151.088145 \n",
       "L 198.940361 150.990066 \n",
       "L 199.550309 151.144429 \n",
       "L 200.160256 151.04698 \n",
       "L 200.770203 151.19971 \n",
       "L 201.38015 150.606492 \n",
       "L 201.990097 151.006908 \n",
       "L 202.600044 150.665791 \n",
       "L 203.209992 150.5726 \n",
       "L 203.819939 150.236379 \n",
       "L 204.429886 150.145872 \n",
       "L 205.039833 149.57271 \n",
       "L 206.259727 149.879025 \n",
       "L 206.869675 149.791608 \n",
       "L 207.479622 150.180103 \n",
       "L 209.309463 150.622199 \n",
       "L 209.91941 150.066301 \n",
       "L 210.529358 149.747676 \n",
       "L 211.139305 149.663358 \n",
       "L 212.359199 149.95626 \n",
       "L 212.969146 150.329694 \n",
       "L 213.579093 150.244373 \n",
       "L 214.189041 149.932823 \n",
       "L 215.408935 150.217623 \n",
       "L 216.018882 149.90995 \n",
       "L 216.628829 150.05129 \n",
       "L 217.238776 149.969125 \n",
       "L 217.848724 148.780136 \n",
       "L 218.458671 148.703672 \n",
       "L 219.068618 148.40806 \n",
       "L 219.678565 148.333659 \n",
       "L 220.288512 148.477865 \n",
       "L 220.898459 148.83811 \n",
       "L 221.508407 148.330254 \n",
       "L 222.118354 148.041817 \n",
       "L 222.728301 147.54096 \n",
       "L 223.338248 147.68544 \n",
       "L 223.948195 147.402794 \n",
       "L 224.558142 147.758889 \n",
       "L 225.16809 147.478115 \n",
       "L 225.778037 147.410051 \n",
       "L 226.997931 146.857459 \n",
       "L 228.217825 146.727999 \n",
       "L 228.827773 146.870664 \n",
       "L 230.047667 146.332246 \n",
       "L 230.657614 146.474787 \n",
       "L 231.267561 146.412646 \n",
       "L 231.877508 145.945151 \n",
       "L 232.487456 145.885387 \n",
       "L 233.097403 146.027489 \n",
       "L 233.70735 145.967858 \n",
       "L 234.317297 146.108643 \n",
       "L 234.927244 146.049153 \n",
       "L 235.537191 146.188637 \n",
       "L 236.147139 146.129279 \n",
       "L 236.757086 145.873201 \n",
       "L 237.367033 145.815385 \n",
       "L 237.97698 145.953725 \n",
       "L 238.586927 145.700961 \n",
       "L 240.416769 146.111418 \n",
       "L 241.026716 145.861603 \n",
       "L 241.636663 146.188637 \n",
       "L 242.24661 146.322371 \n",
       "L 244.686399 146.09441 \n",
       "L 245.296346 146.226206 \n",
       "L 245.906293 145.795535 \n",
       "L 247.126188 145.686604 \n",
       "L 247.736135 145.447368 \n",
       "L 248.346082 145.025014 \n",
       "L 248.956029 145.15773 \n",
       "L 249.565976 144.922603 \n",
       "L 250.175923 144.871903 \n",
       "L 250.785871 145.003815 \n",
       "L 251.395818 144.953181 \n",
       "L 253.835606 145.471277 \n",
       "L 254.445554 145.241195 \n",
       "L 255.665448 145.140672 \n",
       "L 256.275395 144.559723 \n",
       "L 256.885342 144.158967 \n",
       "L 257.495289 144.288542 \n",
       "L 258.105237 144.066538 \n",
       "L 258.715184 144.020767 \n",
       "L 259.325131 143.800999 \n",
       "L 259.935078 143.756338 \n",
       "L 260.545025 143.365564 \n",
       "L 262.374867 143.237273 \n",
       "L 262.984814 143.537158 \n",
       "L 263.594761 143.664671 \n",
       "L 264.204708 143.451366 \n",
       "L 264.814655 143.747863 \n",
       "L 265.424603 143.704586 \n",
       "L 266.644497 143.95474 \n",
       "L 267.254444 143.911231 \n",
       "L 268.474338 144.157906 \n",
       "L 269.084286 144.114181 \n",
       "L 270.30418 144.357452 \n",
       "L 270.914127 144.313528 \n",
       "L 271.524074 144.433858 \n",
       "L 272.134021 144.38996 \n",
       "L 272.743969 144.183289 \n",
       "L 273.963863 144.421904 \n",
       "L 274.57381 144.216941 \n",
       "L 275.183757 144.335457 \n",
       "L 276.403652 144.890874 \n",
       "L 277.623546 145.121328 \n",
       "L 278.84344 145.665943 \n",
       "L 279.453387 145.462106 \n",
       "L 280.063335 145.731903 \n",
       "L 280.673282 145.843129 \n",
       "L 281.283229 145.48391 \n",
       "L 281.893176 145.439034 \n",
       "L 282.503123 145.705874 \n",
       "L 283.11307 145.350043 \n",
       "L 283.723018 145.151061 \n",
       "L 284.332965 145.262047 \n",
       "L 284.942912 145.218413 \n",
       "L 285.552859 145.482179 \n",
       "L 286.162806 145.438172 \n",
       "L 286.772753 145.699884 \n",
       "L 287.382701 145.655529 \n",
       "L 287.992648 145.915219 \n",
       "L 288.602595 145.567541 \n",
       "L 289.212542 145.826055 \n",
       "L 292.262278 146.352593 \n",
       "L 293.482172 145.966259 \n",
       "L 294.092119 146.070353 \n",
       "L 294.702067 145.878959 \n",
       "L 295.312014 145.835648 \n",
       "L 295.921961 146.085952 \n",
       "L 296.531908 145.896033 \n",
       "L 297.141855 145.998941 \n",
       "L 297.751802 145.95578 \n",
       "L 299.581644 146.260843 \n",
       "L 300.801538 146.174272 \n",
       "L 301.411485 146.274612 \n",
       "L 302.021433 146.088595 \n",
       "L 302.63138 146.046088 \n",
       "L 303.241327 145.861603 \n",
       "L 303.851274 145.819891 \n",
       "L 305.681116 146.118261 \n",
       "L 306.291063 146.076326 \n",
       "L 306.90101 146.174636 \n",
       "L 307.510957 146.412141 \n",
       "L 308.120904 146.091105 \n",
       "L 308.730851 146.188637 \n",
       "L 309.340799 146.424327 \n",
       "L 311.17064 146.711563 \n",
       "L 311.780587 146.943641 \n",
       "L 312.390534 146.900695 \n",
       "L 313.000482 146.994565 \n",
       "L 313.610429 146.679187 \n",
       "L 314.220376 146.63721 \n",
       "L 314.830323 146.731031 \n",
       "L 315.44027 146.689129 \n",
       "L 316.050217 146.782377 \n",
       "L 316.660165 146.740558 \n",
       "L 317.880059 146.925448 \n",
       "L 319.099953 146.841917 \n",
       "L 319.7099 146.667448 \n",
       "L 320.929795 146.585748 \n",
       "L 321.539742 146.413135 \n",
       "L 322.149689 146.37308 \n",
       "L 322.759636 146.201784 \n",
       "L 323.369583 146.424658 \n",
       "L 323.979531 146.38486 \n",
       "L 325.199425 146.045417 \n",
       "L 326.419319 146.227515 \n",
       "L 327.029266 146.188637 \n",
       "L 327.639214 146.407924 \n",
       "L 328.859108 146.586668 \n",
       "L 329.469055 146.419216 \n",
       "L 330.079002 146.380345 \n",
       "L 330.688949 146.596675 \n",
       "L 331.298897 146.557581 \n",
       "L 331.908844 146.772519 \n",
       "L 332.518791 146.859836 \n",
       "L 333.128738 147.073109 \n",
       "L 334.348632 147.2452 \n",
       "L 334.95858 147.20517 \n",
       "L 335.568527 147.290532 \n",
       "L 336.788421 146.961485 \n",
       "L 338.008315 146.883579 \n",
       "L 339.22821 146.559271 \n",
       "L 339.838157 146.52147 \n",
       "L 340.448104 146.237838 \n",
       "L 342.887893 146.091105 \n",
       "L 343.49784 146.176475 \n",
       "L 344.107787 146.140082 \n",
       "L 345.327681 146.309497 \n",
       "L 345.937629 146.273054 \n",
       "L 346.547576 146.357108 \n",
       "L 347.157523 146.320723 \n",
       "L 348.377417 145.770177 \n",
       "L 350.207259 145.665943 \n",
       "L 350.817206 145.750037 \n",
       "L 351.427153 145.95206 \n",
       "L 352.0371 145.91715 \n",
       "L 352.647048 145.764601 \n",
       "L 353.256995 145.730238 \n",
       "L 354.476889 145.896033 \n",
       "L 355.086836 145.628009 \n",
       "L 356.916678 145.875264 \n",
       "L 357.526625 145.725342 \n",
       "L 358.136572 145.807216 \n",
       "L 358.746519 145.658056 \n",
       "L 359.356466 145.164208 \n",
       "L 359.966414 145.246729 \n",
       "L 361.186308 145.52515 \n",
       "L 364.236044 145.928209 \n",
       "L 364.845991 145.89484 \n",
       "L 366.675832 146.357108 \n",
       "L 367.28578 146.098967 \n",
       "L 367.895727 146.177453 \n",
       "L 368.505674 146.032344 \n",
       "L 369.725568 146.077444 \n",
       "L 369.725568 146.077444 \n",
       "\" style=\"fill:none;stroke:#d62728;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_20\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 185.105455 \n",
       "L 65.971879 129.51 \n",
       "L 66.581826 148.041817 \n",
       "L 67.191773 157.307725 \n",
       "L 67.80172 162.867274 \n",
       "L 68.411668 138.775908 \n",
       "L 69.021615 121.567793 \n",
       "L 69.631562 122.560567 \n",
       "L 70.241509 123.332728 \n",
       "L 70.851456 118.390912 \n",
       "L 71.461403 109.293474 \n",
       "L 72.071351 110.978183 \n",
       "L 72.681298 120.956854 \n",
       "L 73.291245 121.567793 \n",
       "L 73.901192 125.80364 \n",
       "L 75.121086 139.320962 \n",
       "L 75.731034 144.953181 \n",
       "L 76.340981 147.066457 \n",
       "L 76.950928 140.629088 \n",
       "L 77.560875 142.747012 \n",
       "L 78.170822 137.091199 \n",
       "L 79.390717 141.092392 \n",
       "L 80.610611 140.201433 \n",
       "L 81.220558 143.923641 \n",
       "L 81.830505 143.408867 \n",
       "L 83.660347 147.444017 \n",
       "L 84.880241 146.357108 \n",
       "L 86.710083 154.219089 \n",
       "L 87.32003 150.546123 \n",
       "L 88.539924 152.31839 \n",
       "L 89.149871 154.527955 \n",
       "L 89.759819 153.917762 \n",
       "L 90.369766 152.01292 \n",
       "L 90.979713 152.782513 \n",
       "L 91.58966 154.780662 \n",
       "L 93.419502 156.716288 \n",
       "L 94.029449 154.99125 \n",
       "L 94.639396 154.471224 \n",
       "L 95.249343 151.748185 \n",
       "L 95.85929 153.492351 \n",
       "L 97.079185 152.587358 \n",
       "L 98.299079 149.726534 \n",
       "L 98.909026 149.365518 \n",
       "L 99.518973 149.992537 \n",
       "L 101.958762 148.649417 \n",
       "L 102.568709 146.547317 \n",
       "L 104.398551 148.326923 \n",
       "L 105.008498 148.041817 \n",
       "L 105.618445 146.935439 \n",
       "L 106.228392 148.314348 \n",
       "L 106.838339 148.041817 \n",
       "L 107.448286 146.982859 \n",
       "L 108.058234 146.736764 \n",
       "L 108.668181 148.041817 \n",
       "L 109.278128 148.549541 \n",
       "L 109.888075 149.794831 \n",
       "L 110.498022 149.524362 \n",
       "L 111.107969 148.529501 \n",
       "L 111.717917 149.00451 \n",
       "L 112.937811 148.510977 \n",
       "L 113.547758 148.968407 \n",
       "L 114.157705 150.100913 \n",
       "L 114.767652 149.849806 \n",
       "L 115.3776 148.934921 \n",
       "L 115.987547 148.703672 \n",
       "L 116.597494 149.131924 \n",
       "L 117.207441 148.903764 \n",
       "L 117.817388 148.041817 \n",
       "L 119.037283 147.625378 \n",
       "L 119.64723 146.806369 \n",
       "L 120.257177 146.616292 \n",
       "L 120.867124 147.034653 \n",
       "L 121.477071 148.041817 \n",
       "L 122.087018 146.66179 \n",
       "L 122.696966 145.896033 \n",
       "L 123.91686 145.558172 \n",
       "L 125.136754 147.480253 \n",
       "L 126.356649 147.124406 \n",
       "L 127.576543 148.941425 \n",
       "L 128.796437 149.630262 \n",
       "L 130.626279 149.071365 \n",
       "L 131.846173 149.726534 \n",
       "L 132.45612 149.043538 \n",
       "L 133.676015 148.697814 \n",
       "L 134.285962 149.504861 \n",
       "L 134.895909 149.814431 \n",
       "L 135.505856 149.639391 \n",
       "L 136.115803 148.992166 \n",
       "L 136.72575 148.827067 \n",
       "L 137.945645 149.431702 \n",
       "L 138.555592 148.807599 \n",
       "L 139.165539 149.560822 \n",
       "L 139.775486 149.397802 \n",
       "L 140.385433 149.685775 \n",
       "L 142.215275 149.209175 \n",
       "L 142.825222 147.752262 \n",
       "L 144.045116 147.471612 \n",
       "L 144.655064 147.758889 \n",
       "L 145.265011 148.462994 \n",
       "L 146.484905 149.009903 \n",
       "L 147.094852 148.041817 \n",
       "L 147.704799 147.496763 \n",
       "L 148.314747 148.177092 \n",
       "L 149.534641 147.908496 \n",
       "L 150.144588 148.571304 \n",
       "L 150.754535 148.830406 \n",
       "L 151.364482 149.477382 \n",
       "L 151.97443 148.171409 \n",
       "L 153.804271 148.930332 \n",
       "L 155.024165 147.916607 \n",
       "L 155.634113 147.79307 \n",
       "L 156.24406 148.041817 \n",
       "L 156.854007 147.55091 \n",
       "L 158.073901 148.768555 \n",
       "L 159.293796 148.520057 \n",
       "L 159.903743 148.754579 \n",
       "L 160.51369 148.632003 \n",
       "L 161.123637 147.807237 \n",
       "L 161.733584 147.342508 \n",
       "L 162.343531 147.578522 \n",
       "L 162.953479 147.466293 \n",
       "L 163.563426 148.041817 \n",
       "L 164.173373 147.587055 \n",
       "L 164.78332 146.79883 \n",
       "L 166.003214 147.260361 \n",
       "L 167.223109 147.049043 \n",
       "L 167.833056 147.274229 \n",
       "L 168.443003 147.823797 \n",
       "L 169.05295 147.391577 \n",
       "L 169.662897 147.287616 \n",
       "L 170.272845 147.506216 \n",
       "L 171.492739 146.66517 \n",
       "L 172.102686 146.883579 \n",
       "L 172.712633 146.785426 \n",
       "L 173.32258 146.376037 \n",
       "L 174.542475 146.806369 \n",
       "L 175.152422 146.403649 \n",
       "L 175.762369 146.616292 \n",
       "L 176.982263 147.638956 \n",
       "L 177.592211 147.54096 \n",
       "L 178.202158 147.145117 \n",
       "L 178.812105 147.645418 \n",
       "L 179.422052 147.253228 \n",
       "L 180.031999 147.159349 \n",
       "L 180.641946 147.359069 \n",
       "L 181.251894 147.265621 \n",
       "L 181.861841 146.594024 \n",
       "L 182.471788 146.793561 \n",
       "L 183.081735 146.704471 \n",
       "L 183.691682 146.046088 \n",
       "L 184.911577 145.878205 \n",
       "L 185.521524 144.953181 \n",
       "L 186.131471 145.154955 \n",
       "L 186.741418 145.076725 \n",
       "L 187.351365 144.722685 \n",
       "L 187.961312 144.922603 \n",
       "L 188.57126 144.846677 \n",
       "L 189.181207 144.226443 \n",
       "L 189.791154 143.883462 \n",
       "L 190.401101 143.813682 \n",
       "L 191.011048 142.938853 \n",
       "L 191.620995 142.874293 \n",
       "L 192.230943 143.076357 \n",
       "L 192.84089 143.011756 \n",
       "L 194.060784 143.408867 \n",
       "L 196.500573 143.15148 \n",
       "L 197.720467 143.53638 \n",
       "L 198.330414 143.218467 \n",
       "L 198.940361 143.15616 \n",
       "L 199.550309 142.591282 \n",
       "L 200.160256 142.782792 \n",
       "L 200.770203 142.473968 \n",
       "L 201.38015 142.664284 \n",
       "L 201.990097 143.100001 \n",
       "L 202.600044 142.793868 \n",
       "L 203.209992 142.735356 \n",
       "L 203.819939 142.433507 \n",
       "L 204.429886 142.86262 \n",
       "L 205.039833 142.804564 \n",
       "L 205.64978 142.987689 \n",
       "L 206.259727 142.450324 \n",
       "L 206.869675 142.156179 \n",
       "L 207.479622 142.102132 \n",
       "L 208.699516 142.46657 \n",
       "L 209.309463 142.177321 \n",
       "L 210.529358 142.536548 \n",
       "L 213.579093 142.269617 \n",
       "L 214.798988 142.617875 \n",
       "L 215.408935 142.339719 \n",
       "L 217.238776 142.185763 \n",
       "L 217.848724 142.578259 \n",
       "L 219.678565 143.080549 \n",
       "L 220.288512 143.02733 \n",
       "L 221.508407 143.787429 \n",
       "L 222.118354 143.947583 \n",
       "L 222.728301 143.891837 \n",
       "L 223.338248 144.05035 \n",
       "L 223.948195 143.78163 \n",
       "L 224.558142 143.72716 \n",
       "L 225.16809 143.884489 \n",
       "L 225.778037 143.830044 \n",
       "L 226.997931 144.140385 \n",
       "L 227.607878 144.502031 \n",
       "L 228.827773 144.390573 \n",
       "L 229.43772 144.541365 \n",
       "L 230.657614 144.430843 \n",
       "L 231.267561 144.579829 \n",
       "L 231.877508 144.524829 \n",
       "L 232.487456 144.268063 \n",
       "L 234.927244 144.853553 \n",
       "L 235.537191 145.195863 \n",
       "L 236.757086 145.478907 \n",
       "L 237.367033 145.422482 \n",
       "L 237.97698 145.757966 \n",
       "L 238.586927 145.896033 \n",
       "L 239.196874 145.644346 \n",
       "L 239.806822 145.588128 \n",
       "L 241.026716 146.246346 \n",
       "L 241.636663 146.380345 \n",
       "L 243.466505 146.207616 \n",
       "L 244.686399 146.471324 \n",
       "L 248.346082 146.133231 \n",
       "L 248.956029 146.262277 \n",
       "L 249.565976 146.023504 \n",
       "L 250.175923 146.152061 \n",
       "L 250.785871 145.915219 \n",
       "L 251.395818 146.043288 \n",
       "L 252.005765 145.989439 \n",
       "L 252.615712 146.116439 \n",
       "L 253.225659 146.06269 \n",
       "L 253.835606 146.188637 \n",
       "L 254.445554 146.135012 \n",
       "L 255.055501 145.90353 \n",
       "L 256.275395 145.799114 \n",
       "L 256.885342 146.100392 \n",
       "L 257.495289 146.047894 \n",
       "L 258.105237 146.346479 \n",
       "L 258.715184 146.293533 \n",
       "L 259.325131 146.066641 \n",
       "L 260.545025 146.656265 \n",
       "L 262.374867 146.497503 \n",
       "L 262.984814 146.787356 \n",
       "L 263.594761 146.904895 \n",
       "L 264.204708 146.851701 \n",
       "L 264.814655 147.137827 \n",
       "L 265.424603 147.253228 \n",
       "L 266.03455 147.030991 \n",
       "L 266.644497 147.14602 \n",
       "L 267.254444 147.427813 \n",
       "L 269.084286 147.765227 \n",
       "L 270.30418 147.656884 \n",
       "L 270.914127 147.438715 \n",
       "L 271.524074 147.713822 \n",
       "L 272.134021 147.823797 \n",
       "L 272.743969 147.607053 \n",
       "L 273.353916 147.716697 \n",
       "L 273.963863 147.501535 \n",
       "L 274.57381 147.449236 \n",
       "L 275.183757 147.558382 \n",
       "L 275.793704 147.345541 \n",
       "L 276.403652 147.454356 \n",
       "L 277.013599 147.722305 \n",
       "L 277.623546 147.351522 \n",
       "L 278.233493 147.141704 \n",
       "L 279.453387 147.357404 \n",
       "L 280.063335 146.991856 \n",
       "L 281.283229 147.206587 \n",
       "L 281.893176 147.156872 \n",
       "L 283.11307 147.679467 \n",
       "L 283.723018 147.628858 \n",
       "L 284.332965 147.424093 \n",
       "L 285.552859 147.632279 \n",
       "L 286.162806 147.582349 \n",
       "L 286.772753 147.074501 \n",
       "L 287.992648 147.282322 \n",
       "L 288.602595 147.233892 \n",
       "L 289.212542 147.034653 \n",
       "L 289.822489 147.288494 \n",
       "L 290.432436 147.240445 \n",
       "L 291.042384 147.492356 \n",
       "L 291.652331 147.294567 \n",
       "L 292.262278 147.544987 \n",
       "L 292.872225 147.645418 \n",
       "L 293.482172 147.448805 \n",
       "L 294.092119 147.401095 \n",
       "L 294.702067 147.501104 \n",
       "L 295.312014 147.453511 \n",
       "L 296.531908 147.066457 \n",
       "L 297.751802 146.974542 \n",
       "L 298.36175 147.074103 \n",
       "L 299.581644 146.982859 \n",
       "L 300.801538 147.179878 \n",
       "L 301.411485 146.991044 \n",
       "L 302.021433 146.94611 \n",
       "L 305.071168 147.430364 \n",
       "L 305.681116 147.103496 \n",
       "L 306.291063 147.199462 \n",
       "L 307.510957 146.132767 \n",
       "L 308.730851 146.327624 \n",
       "L 309.340799 146.285688 \n",
       "L 309.950746 146.382251 \n",
       "L 311.780587 146.257273 \n",
       "L 312.390534 146.489898 \n",
       "L 313.610429 146.679187 \n",
       "L 315.44027 146.553861 \n",
       "L 316.050217 146.782377 \n",
       "L 316.660165 146.875171 \n",
       "L 317.270112 147.101798 \n",
       "L 317.880059 147.193373 \n",
       "L 318.490006 146.883579 \n",
       "L 319.099953 146.975238 \n",
       "L 320.929795 146.850492 \n",
       "L 321.539742 147.073407 \n",
       "L 322.149689 147.163533 \n",
       "L 322.759636 147.384659 \n",
       "L 324.589478 147.650306 \n",
       "L 325.199425 147.607815 \n",
       "L 325.809372 147.435641 \n",
       "L 326.419319 147.393855 \n",
       "L 327.029266 147.481553 \n",
       "L 327.639214 147.439858 \n",
       "L 330.079002 147.786211 \n",
       "L 330.688949 147.616779 \n",
       "L 331.908844 147.534101 \n",
       "L 332.518791 147.746322 \n",
       "L 333.128738 147.831228 \n",
       "L 333.738685 148.041817 \n",
       "L 334.95858 148.209153 \n",
       "L 335.568527 148.041817 \n",
       "L 336.178474 147.750306 \n",
       "L 336.788421 147.709407 \n",
       "L 337.398368 147.544324 \n",
       "L 338.008315 147.504062 \n",
       "L 338.618263 147.587809 \n",
       "L 339.22821 147.547638 \n",
       "L 339.838157 147.630912 \n",
       "L 340.448104 147.83682 \n",
       "L 341.667998 147.756089 \n",
       "L 342.277946 147.83817 \n",
       "L 342.887893 147.554141 \n",
       "L 343.49784 147.514658 \n",
       "L 344.717734 147.193961 \n",
       "L 345.327681 147.155514 \n",
       "L 346.547576 146.838454 \n",
       "L 347.76747 146.763762 \n",
       "L 348.377417 146.846217 \n",
       "L 348.987365 146.689717 \n",
       "L 349.597312 146.414833 \n",
       "L 350.817206 146.816898 \n",
       "L 351.427153 146.66179 \n",
       "L 352.647048 146.824686 \n",
       "L 353.256995 146.553008 \n",
       "L 353.866942 146.517046 \n",
       "L 354.476889 146.364199 \n",
       "L 355.696783 146.293533 \n",
       "L 356.306731 146.374729 \n",
       "L 357.526625 146.304461 \n",
       "L 358.136572 146.500709 \n",
       "L 358.746519 146.350116 \n",
       "L 359.966414 146.625132 \n",
       "L 360.576361 146.245956 \n",
       "L 361.186308 146.325909 \n",
       "L 362.406202 146.256991 \n",
       "L 363.626097 146.415554 \n",
       "L 364.236044 146.607586 \n",
       "L 364.845991 146.572833 \n",
       "L 365.455938 146.650996 \n",
       "L 366.065885 146.841379 \n",
       "L 366.675832 146.806369 \n",
       "L 369.725568 147.189355 \n",
       "L 369.725568 147.189355 \n",
       "\" style=\"fill:none;stroke:#9467bd;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_21\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 65.361932 18.319091 \n",
       "L 65.971879 101.712275 \n",
       "L 66.581826 73.914541 \n",
       "L 67.191773 101.712275 \n",
       "L 67.80172 107.271823 \n",
       "L 68.411668 120.244092 \n",
       "L 69.021615 129.51 \n",
       "L 69.631562 143.408867 \n",
       "L 70.241509 148.041817 \n",
       "L 70.851456 157.307725 \n",
       "L 72.071351 152.674775 \n",
       "L 72.681298 155.169439 \n",
       "L 73.291245 149.365518 \n",
       "L 73.901192 148.041817 \n",
       "L 74.511139 150.3583 \n",
       "L 75.121086 145.861603 \n",
       "L 75.731034 144.953181 \n",
       "L 76.340981 141.214304 \n",
       "L 76.950928 143.408867 \n",
       "L 77.560875 142.747012 \n",
       "L 78.170822 144.672399 \n",
       "L 78.780769 144.013162 \n",
       "L 79.390717 138.775908 \n",
       "L 80.000664 142.852911 \n",
       "L 80.610611 140.201433 \n",
       "L 81.220558 139.805457 \n",
       "L 81.830505 141.423311 \n",
       "L 82.440452 137.178343 \n",
       "L 83.0504 135.069548 \n",
       "L 83.660347 138.477008 \n",
       "L 85.490188 142.591282 \n",
       "L 86.100135 143.805978 \n",
       "L 87.32003 143.03322 \n",
       "L 87.929977 139.751268 \n",
       "L 88.539924 139.488671 \n",
       "L 89.149871 137.849318 \n",
       "L 89.759819 140.357891 \n",
       "L 90.369766 141.423311 \n",
       "L 90.979713 141.146257 \n",
       "L 91.58966 138.354731 \n",
       "L 92.199607 136.922728 \n",
       "L 92.809554 137.970179 \n",
       "L 93.419502 140.155943 \n",
       "L 94.029449 138.775908 \n",
       "L 95.249343 140.629088 \n",
       "L 95.85929 140.411069 \n",
       "L 96.469237 139.132294 \n",
       "L 97.079185 138.950742 \n",
       "L 97.689132 137.746369 \n",
       "L 98.299079 139.618263 \n",
       "L 98.909026 138.444989 \n",
       "L 100.12892 138.136885 \n",
       "L 101.348815 139.702498 \n",
       "L 101.958762 141.358212 \n",
       "L 102.568709 142.063817 \n",
       "L 103.788603 141.67151 \n",
       "L 106.228392 144.226443 \n",
       "L 106.838339 144.818891 \n",
       "L 108.058234 144.387657 \n",
       "L 109.278128 145.503213 \n",
       "L 109.888075 144.535798 \n",
       "L 110.498022 142.852911 \n",
       "L 111.107969 142.677349 \n",
       "L 111.717917 143.228359 \n",
       "L 112.327864 143.052482 \n",
       "L 113.547758 145.493694 \n",
       "L 114.157705 145.296369 \n",
       "L 114.767652 146.459834 \n",
       "L 115.3776 145.585792 \n",
       "L 115.987547 146.056269 \n",
       "L 116.597494 147.169738 \n",
       "L 117.207441 146.964385 \n",
       "L 117.817388 148.041817 \n",
       "L 118.427335 147.831228 \n",
       "L 119.037283 148.250044 \n",
       "L 119.64723 148.041817 \n",
       "L 120.257177 149.060048 \n",
       "L 120.867124 149.451849 \n",
       "L 121.477071 148.041817 \n",
       "L 122.087018 148.436111 \n",
       "L 122.696966 147.066457 \n",
       "L 123.306913 146.304461 \n",
       "L 123.91686 146.131326 \n",
       "L 125.136754 144.672399 \n",
       "L 125.746701 144.520778 \n",
       "L 126.356649 144.922603 \n",
       "L 126.966596 143.681389 \n",
       "L 130.626279 142.894093 \n",
       "L 131.236226 143.791406 \n",
       "L 131.846173 143.661573 \n",
       "L 132.45612 144.034941 \n",
       "L 133.066067 143.408867 \n",
       "L 133.676015 144.269853 \n",
       "L 134.285962 144.140385 \n",
       "L 135.505856 145.80522 \n",
       "L 136.115803 145.190768 \n",
       "L 136.72575 146.000176 \n",
       "L 137.335698 145.861603 \n",
       "L 137.945645 146.188637 \n",
       "L 139.165539 145.915219 \n",
       "L 139.775486 144.877851 \n",
       "L 140.385433 144.305567 \n",
       "L 140.995381 144.1872 \n",
       "L 141.605328 144.511947 \n",
       "L 142.215275 144.39382 \n",
       "L 143.435169 145.886953 \n",
       "L 144.045116 145.760981 \n",
       "L 144.655064 145.212531 \n",
       "L 145.265011 145.514753 \n",
       "L 145.874958 146.23044 \n",
       "L 147.094852 146.806369 \n",
       "L 147.704799 147.496763 \n",
       "L 148.314747 146.959671 \n",
       "L 148.924694 145.624629 \n",
       "L 150.754535 145.281764 \n",
       "L 151.364482 144.779176 \n",
       "L 152.584377 144.567104 \n",
       "L 153.194324 144.079843 \n",
       "L 153.804271 143.980049 \n",
       "L 155.024165 143.03322 \n",
       "L 155.634113 142.942457 \n",
       "L 156.854007 142.028186 \n",
       "L 157.463954 142.311586 \n",
       "L 158.073901 141.501176 \n",
       "L 159.293796 142.063817 \n",
       "L 159.903743 141.626957 \n",
       "L 160.51369 141.54978 \n",
       "L 161.123637 141.825451 \n",
       "L 161.733584 142.447308 \n",
       "L 162.343531 142.713924 \n",
       "L 162.953479 142.2866 \n",
       "L 163.563426 142.207733 \n",
       "L 164.78332 142.730874 \n",
       "L 166.003214 142.571582 \n",
       "L 166.613162 143.159184 \n",
       "L 167.223109 142.747012 \n",
       "L 167.833056 142.668692 \n",
       "L 168.443003 142.264249 \n",
       "L 169.05295 142.514785 \n",
       "L 169.662897 142.439173 \n",
       "L 170.272845 141.721722 \n",
       "L 170.882792 142.290568 \n",
       "L 171.492739 142.217533 \n",
       "L 172.102686 142.461218 \n",
       "L 172.712633 141.759847 \n",
       "L 173.32258 141.691028 \n",
       "L 173.932528 141.312391 \n",
       "L 174.542475 141.555687 \n",
       "L 175.152422 141.48913 \n",
       "L 178.202158 142.661617 \n",
       "L 178.812105 142.293981 \n",
       "L 180.641946 142.092133 \n",
       "L 181.251894 141.153025 \n",
       "L 181.861841 140.513265 \n",
       "L 182.471788 140.168196 \n",
       "L 184.911577 141.080628 \n",
       "L 185.521524 141.583762 \n",
       "L 186.131471 141.802461 \n",
       "L 186.741418 142.296955 \n",
       "L 187.351365 142.23334 \n",
       "L 187.961312 142.445577 \n",
       "L 188.57126 142.929591 \n",
       "L 189.181207 143.136336 \n",
       "L 189.791154 142.798673 \n",
       "L 191.620995 143.408867 \n",
       "L 192.230943 142.544343 \n",
       "L 192.84089 142.217533 \n",
       "L 193.450837 142.157306 \n",
       "L 194.060784 142.359892 \n",
       "L 194.670731 142.038558 \n",
       "L 195.280678 141.980012 \n",
       "L 195.890626 142.180593 \n",
       "L 196.500573 142.121932 \n",
       "L 197.11052 141.807614 \n",
       "L 197.720467 141.751206 \n",
       "L 198.330414 141.949169 \n",
       "L 198.940361 141.892629 \n",
       "L 200.160256 142.782792 \n",
       "L 201.38015 143.160667 \n",
       "L 201.990097 142.605822 \n",
       "L 202.600044 142.793868 \n",
       "L 203.209992 142.735356 \n",
       "L 203.819939 143.165025 \n",
       "L 204.429886 142.619847 \n",
       "L 205.64978 143.469036 \n",
       "L 206.259727 143.6485 \n",
       "L 208.089569 143.468009 \n",
       "L 208.699516 143.880015 \n",
       "L 209.309463 144.053962 \n",
       "L 209.91941 144.460037 \n",
       "L 210.529358 144.39749 \n",
       "L 211.139305 144.567104 \n",
       "L 212.359199 145.3616 \n",
       "L 212.969146 144.83879 \n",
       "L 214.189041 145.167497 \n",
       "L 214.798988 144.651853 \n",
       "L 215.408935 144.815635 \n",
       "L 216.018882 144.753917 \n",
       "L 216.628829 144.246143 \n",
       "L 217.238776 143.964822 \n",
       "L 217.848724 144.350219 \n",
       "L 218.458671 144.511947 \n",
       "L 219.068618 144.892141 \n",
       "L 219.678565 144.831583 \n",
       "L 220.288512 144.989524 \n",
       "L 220.898459 144.494715 \n",
       "L 221.508407 144.869053 \n",
       "L 222.728301 145.179766 \n",
       "L 223.338248 145.119498 \n",
       "L 223.948195 145.485708 \n",
       "L 224.558142 145.636931 \n",
       "L 225.16809 145.364218 \n",
       "L 226.387984 145.664153 \n",
       "L 226.997931 146.021433 \n",
       "L 227.607878 145.751371 \n",
       "L 228.217825 145.690771 \n",
       "L 228.827773 145.010591 \n",
       "L 229.43772 144.747273 \n",
       "L 230.047667 145.101347 \n",
       "L 230.657614 145.248419 \n",
       "L 231.267561 145.190768 \n",
       "L 233.097403 146.228924 \n",
       "L 233.70735 146.369269 \n",
       "L 234.317297 146.108643 \n",
       "L 234.927244 146.447681 \n",
       "L 235.537191 146.585748 \n",
       "L 236.147139 146.920677 \n",
       "L 236.757086 146.858942 \n",
       "L 237.367033 147.190532 \n",
       "L 238.586927 146.676321 \n",
       "L 239.196874 147.005078 \n",
       "L 239.806822 146.944113 \n",
       "L 240.416769 146.690545 \n",
       "L 241.026716 146.631097 \n",
       "L 241.636663 146.380345 \n",
       "L 243.466505 146.207616 \n",
       "L 244.076452 145.96172 \n",
       "L 244.686399 146.09441 \n",
       "L 245.296346 145.85056 \n",
       "L 245.906293 145.795535 \n",
       "L 246.51624 146.114011 \n",
       "L 247.126188 146.058481 \n",
       "L 248.346082 146.317931 \n",
       "L 248.956029 146.630459 \n",
       "L 249.565976 146.757433 \n",
       "L 250.175923 146.700702 \n",
       "L 250.785871 146.826616 \n",
       "L 251.395818 146.770025 \n",
       "L 252.005765 146.894896 \n",
       "L 252.615712 146.657946 \n",
       "L 253.225659 146.782377 \n",
       "L 253.835606 147.085337 \n",
       "L 254.445554 147.028829 \n",
       "L 255.665448 147.627366 \n",
       "L 256.275395 147.746728 \n",
       "L 256.885342 147.688836 \n",
       "L 257.495289 147.807237 \n",
       "L 258.105237 147.749519 \n",
       "L 258.715184 147.517333 \n",
       "L 259.325131 147.460884 \n",
       "L 260.545025 147.695431 \n",
       "L 261.76492 148.271319 \n",
       "L 262.374867 148.385005 \n",
       "L 262.984814 148.155859 \n",
       "L 263.594761 148.43974 \n",
       "L 264.204708 148.381857 \n",
       "L 264.814655 148.154816 \n",
       "L 265.424603 148.098151 \n",
       "L 266.03455 148.378759 \n",
       "L 266.644497 148.489719 \n",
       "L 267.254444 148.265097 \n",
       "L 267.864391 148.208772 \n",
       "L 269.694233 148.538208 \n",
       "L 270.30418 148.481742 \n",
       "L 271.524074 147.713822 \n",
       "L 273.353916 148.041817 \n",
       "L 273.963863 147.825702 \n",
       "L 274.57381 147.934079 \n",
       "L 275.183757 147.71953 \n",
       "L 276.403652 147.935006 \n",
       "L 277.013599 147.722305 \n",
       "L 277.623546 147.829422 \n",
       "L 278.233493 148.09477 \n",
       "L 278.84344 147.725039 \n",
       "L 279.453387 147.831228 \n",
       "L 280.063335 148.094315 \n",
       "L 280.673282 148.041817 \n",
       "L 281.283229 148.146225 \n",
       "L 281.893176 148.406213 \n",
       "L 283.11307 148.300645 \n",
       "L 284.332965 148.505112 \n",
       "L 284.942912 148.144485 \n",
       "L 285.552859 147.93943 \n",
       "L 286.162806 147.888664 \n",
       "L 286.772753 147.990909 \n",
       "L 287.382701 148.244908 \n",
       "L 287.992648 147.889923 \n",
       "L 288.602595 148.142812 \n",
       "L 289.212542 148.092177 \n",
       "L 289.822489 148.192485 \n",
       "L 290.432436 148.442507 \n",
       "L 291.042384 148.241627 \n",
       "L 291.652331 148.191267 \n",
       "L 292.262278 147.843083 \n",
       "L 293.482172 148.041817 \n",
       "L 294.092119 147.844674 \n",
       "L 295.312014 148.041817 \n",
       "L 295.921961 147.846231 \n",
       "L 296.531908 147.797983 \n",
       "L 297.751802 147.993304 \n",
       "L 298.36175 147.65473 \n",
       "L 298.971697 147.897039 \n",
       "L 299.581644 147.84928 \n",
       "L 300.191591 147.513713 \n",
       "L 300.801538 147.754507 \n",
       "L 301.411485 147.707485 \n",
       "L 302.021433 147.803625 \n",
       "L 302.63138 148.041817 \n",
       "L 303.241327 147.994422 \n",
       "L 303.851274 148.089096 \n",
       "L 304.461221 147.900353 \n",
       "L 305.071168 147.853679 \n",
       "L 305.681116 147.947988 \n",
       "L 306.291063 147.90143 \n",
       "L 306.90101 148.135182 \n",
       "L 307.510957 148.228066 \n",
       "L 308.120904 148.041817 \n",
       "L 308.730851 148.134477 \n",
       "L 309.340799 148.088035 \n",
       "L 309.950746 148.180116 \n",
       "L 310.560693 148.13379 \n",
       "L 311.17064 148.225299 \n",
       "L 312.390534 147.859238 \n",
       "L 313.000482 147.814154 \n",
       "L 313.610429 147.905556 \n",
       "L 314.220376 147.86058 \n",
       "L 315.44027 148.041817 \n",
       "L 316.660165 147.682847 \n",
       "L 317.880059 147.595273 \n",
       "L 319.099953 148.041817 \n",
       "L 319.7099 147.997487 \n",
       "L 320.319848 148.086047 \n",
       "L 321.539742 147.997802 \n",
       "L 322.149689 147.822248 \n",
       "L 322.759636 147.778954 \n",
       "L 325.809372 148.215018 \n",
       "L 327.639214 148.084821 \n",
       "L 328.249161 148.299204 \n",
       "L 328.859108 148.38421 \n",
       "L 329.469055 148.212616 \n",
       "L 330.079002 148.169628 \n",
       "L 330.688949 148.381857 \n",
       "L 331.298897 148.465885 \n",
       "L 331.908844 148.422608 \n",
       "L 332.518791 147.999608 \n",
       "L 333.128738 147.831228 \n",
       "L 333.738685 147.411484 \n",
       "L 334.95858 147.33067 \n",
       "L 337.398368 147.668697 \n",
       "L 338.008315 147.628162 \n",
       "L 338.618263 147.711635 \n",
       "L 339.22821 147.918272 \n",
       "L 339.838157 147.877455 \n",
       "L 340.448104 148.082816 \n",
       "L 341.667998 148.24591 \n",
       "L 342.887893 148.163738 \n",
       "L 343.49784 148.366224 \n",
       "L 344.107787 148.203669 \n",
       "L 345.327681 148.364112 \n",
       "L 346.547576 148.282494 \n",
       "L 347.157523 148.121869 \n",
       "L 348.377417 148.280937 \n",
       "L 348.987365 148.240658 \n",
       "L 350.207259 148.398202 \n",
       "L 350.817206 148.357923 \n",
       "L 351.427153 148.199535 \n",
       "L 352.0371 148.277896 \n",
       "L 352.647048 147.88477 \n",
       "L 353.256995 148.081002 \n",
       "L 353.866942 147.924527 \n",
       "L 355.086836 148.080753 \n",
       "L 355.696783 147.925264 \n",
       "L 356.306731 148.119358 \n",
       "L 357.526625 148.041817 \n",
       "L 359.356466 148.272031 \n",
       "L 359.966414 148.118398 \n",
       "L 360.576361 148.080033 \n",
       "L 361.186308 147.927426 \n",
       "L 361.796255 148.117925 \n",
       "L 362.406202 148.079792 \n",
       "L 363.016149 148.155511 \n",
       "L 363.626097 148.117461 \n",
       "L 364.236044 147.853107 \n",
       "L 364.845991 147.928818 \n",
       "L 366.065885 147.741707 \n",
       "L 367.28578 148.116542 \n",
       "L 367.895727 147.855385 \n",
       "L 369.725568 147.634118 \n",
       "L 369.725568 147.634118 \n",
       "\" style=\"fill:none;stroke:#8c564b;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_22\">\n",
       "    <path clip-path=\"url(#p69991f9d0c)\" d=\"M 50.14375 147.856501 \n",
       "L 384.94375 147.856501 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 50.14375 251.82 \n",
       "L 50.14375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 384.94375 251.82 \n",
       "L 384.94375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 50.14375 251.82 \n",
       "L 384.94375 251.82 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 50.14375 7.2 \n",
       "L 384.94375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"M 302.089063 103.26875 \n",
       "L 377.94375 103.26875 \n",
       "Q 379.94375 103.26875 379.94375 101.26875 \n",
       "L 379.94375 14.2 \n",
       "Q 379.94375 12.2 377.94375 12.2 \n",
       "L 302.089063 12.2 \n",
       "Q 300.089063 12.2 300.089063 14.2 \n",
       "L 300.089063 101.26875 \n",
       "Q 300.089063 103.26875 302.089063 103.26875 \n",
       "z\n",
       "\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_23\">\n",
       "     <path d=\"M 304.089063 20.298437 \n",
       "L 324.089063 20.298437 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_24\"/>\n",
       "    <g id=\"text_18\">\n",
       "     <!-- P(die=1) -->\n",
       "     <g transform=\"translate(332.089063 23.798437)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 19.671875 64.796875 \n",
       "L 19.671875 37.40625 \n",
       "L 32.078125 37.40625 \n",
       "Q 38.96875 37.40625 42.71875 40.96875 \n",
       "Q 46.484375 44.53125 46.484375 51.125 \n",
       "Q 46.484375 57.671875 42.71875 61.234375 \n",
       "Q 38.96875 64.796875 32.078125 64.796875 \n",
       "z\n",
       "M 9.8125 72.90625 \n",
       "L 32.078125 72.90625 \n",
       "Q 44.34375 72.90625 50.609375 67.359375 \n",
       "Q 56.890625 61.8125 56.890625 51.125 \n",
       "Q 56.890625 40.328125 50.609375 34.8125 \n",
       "Q 44.34375 29.296875 32.078125 29.296875 \n",
       "L 19.671875 29.296875 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-80\"/>\n",
       "       <path d=\"M 31 75.875 \n",
       "Q 24.46875 64.65625 21.28125 53.65625 \n",
       "Q 18.109375 42.671875 18.109375 31.390625 \n",
       "Q 18.109375 20.125 21.3125 9.0625 \n",
       "Q 24.515625 -2 31 -13.1875 \n",
       "L 23.1875 -13.1875 \n",
       "Q 15.875 -1.703125 12.234375 9.375 \n",
       "Q 8.59375 20.453125 8.59375 31.390625 \n",
       "Q 8.59375 42.28125 12.203125 53.3125 \n",
       "Q 15.828125 64.359375 23.1875 75.875 \n",
       "z\n",
       "\" id=\"DejaVuSans-40\"/>\n",
       "       <path d=\"M 10.59375 45.40625 \n",
       "L 73.1875 45.40625 \n",
       "L 73.1875 37.203125 \n",
       "L 10.59375 37.203125 \n",
       "z\n",
       "M 10.59375 25.484375 \n",
       "L 73.1875 25.484375 \n",
       "L 73.1875 17.1875 \n",
       "L 10.59375 17.1875 \n",
       "z\n",
       "\" id=\"DejaVuSans-61\"/>\n",
       "       <path d=\"M 8.015625 75.875 \n",
       "L 15.828125 75.875 \n",
       "Q 23.140625 64.359375 26.78125 53.3125 \n",
       "Q 30.421875 42.28125 30.421875 31.390625 \n",
       "Q 30.421875 20.453125 26.78125 9.375 \n",
       "Q 23.140625 -1.703125 15.828125 -13.1875 \n",
       "L 8.015625 -13.1875 \n",
       "Q 14.5 -2 17.703125 9.0625 \n",
       "Q 20.90625 20.125 20.90625 31.390625 \n",
       "Q 20.90625 42.671875 17.703125 53.65625 \n",
       "Q 14.5 64.65625 8.015625 75.875 \n",
       "z\n",
       "\" id=\"DejaVuSans-41\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_25\">\n",
       "     <path d=\"M 304.089063 34.976562 \n",
       "L 324.089063 34.976562 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_26\"/>\n",
       "    <g id=\"text_19\">\n",
       "     <!-- P(die=2) -->\n",
       "     <g transform=\"translate(332.089063 38.476562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_27\">\n",
       "     <path d=\"M 304.089063 49.654687 \n",
       "L 324.089063 49.654687 \n",
       "\" style=\"fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_28\"/>\n",
       "    <g id=\"text_20\">\n",
       "     <!-- P(die=3) -->\n",
       "     <g transform=\"translate(332.089063 53.154687)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_29\">\n",
       "     <path d=\"M 304.089063 64.332812 \n",
       "L 324.089063 64.332812 \n",
       "\" style=\"fill:none;stroke:#d62728;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_30\"/>\n",
       "    <g id=\"text_21\">\n",
       "     <!-- P(die=4) -->\n",
       "     <g transform=\"translate(332.089063 67.832812)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_31\">\n",
       "     <path d=\"M 304.089063 79.010937 \n",
       "L 324.089063 79.010937 \n",
       "\" style=\"fill:none;stroke:#9467bd;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_32\"/>\n",
       "    <g id=\"text_22\">\n",
       "     <!-- P(die=5) -->\n",
       "     <g transform=\"translate(332.089063 82.510937)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_33\">\n",
       "     <path d=\"M 304.089063 93.689062 \n",
       "L 324.089063 93.689062 \n",
       "\" style=\"fill:none;stroke:#8c564b;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_34\"/>\n",
       "    <g id=\"text_23\">\n",
       "     <!-- P(die=6) -->\n",
       "     <g transform=\"translate(332.089063 97.189062)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-80\"/>\n",
       "      <use x=\"60.302734\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"99.316406\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"162.792969\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"190.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"252.099609\" xlink:href=\"#DejaVuSans-61\"/>\n",
       "      <use x=\"335.888672\" xlink:href=\"#DejaVuSans-54\"/>\n",
       "      <use x=\"399.511719\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p69991f9d0c\">\n",
       "   <rect height=\"244.62\" width=\"334.8\" x=\"50.14375\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts = multinomial.Multinomial(10, fair_probs).sample((500,))\n",
    "cum_counts = counts.cumsum(dim=0)\n",
    "estimates = cum_counts / cum_counts.sum(dim=1, keepdims=True)\n",
    "\n",
    "d2l.set_figsize((6, 4.5))\n",
    "for i in range(6):\n",
    "    d2l.plt.plot(estimates[:, i].numpy(),\n",
    "                 label=(\"P(die=\" + str(i + 1) + \")\"))\n",
    "d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
    "d2l.plt.gca().set_xlabel('Groups of experiments')\n",
    "d2l.plt.gca().set_ylabel('Estimated probability')\n",
    "d2l.plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 20
   },
   "source": [
    "每条实线对应于骰子的6个值中的一个，并给出骰子在每组实验后出现值的估计概率。\n",
    "当我们通过更多的实验获得更多的数据时，这$6$条实体曲线向真实概率收敛。\n",
    "\n",
    "### 概率论公理\n",
    "\n",
    "在处理骰子掷出时，我们将集合$\\mathcal{S} = \\{1, 2, 3, 4, 5, 6\\}$\n",
    "称为*样本空间*（sample space）或*结果空间*（outcome space），\n",
    "其中每个元素都是*结果*（outcome）。\n",
    "*事件*（event）是一组给定样本空间的随机结果。\n",
    "例如，“看到$5$”（$\\{5\\}$）和“看到奇数”（$\\{1, 3, 5\\}$）都是掷出骰子的有效事件。\n",
    "注意，如果一个随机实验的结果在$\\mathcal{A}$中，则事件$\\mathcal{A}$已经发生。\n",
    "也就是说，如果投掷出$3$点，因为$3 \\in \\{1, 3, 5\\}$，我们可以说，“看到奇数”的事件发生了。\n",
    "\n",
    "*概率*（probability）可以被认为是将集合映射到真实值的函数。\n",
    "在给定的样本空间$\\mathcal{S}$中，事件$\\mathcal{A}$的概率，\n",
    "表示为$P(\\mathcal{A})$，满足以下属性：\n",
    "\n",
    "* 对于任意事件$\\mathcal{A}$，其概率从不会是负数，即$P(\\mathcal{A}) \\geq 0$；\n",
    "* 整个样本空间的概率为$1$，即$P(\\mathcal{S}) = 1$；\n",
    "* 对于*互斥*（mutually exclusive）事件（对于所有$i \\neq j$都有$\\mathcal{A}_i \\cap \\mathcal{A}_j = \\emptyset$）的任意一个可数序列$\\mathcal{A}_1, \\mathcal{A}_2, \\ldots$，序列中任意一个事件发生的概率等于它们各自发生的概率之和，即$P(\\bigcup_{i=1}^{\\infty} \\mathcal{A}_i) = \\sum_{i=1}^{\\infty} P(\\mathcal{A}_i)$。\n",
    "\n",
    "以上也是概率论的公理，由科尔莫戈罗夫于1933年提出。\n",
    "有了这个公理系统，我们可以避免任何关于随机性的哲学争论；\n",
    "相反，我们可以用数学语言严格地推理。\n",
    "例如，假设事件$\\mathcal{A}_1$为整个样本空间，\n",
    "且当所有$i > 1$时的$\\mathcal{A}_i = \\emptyset$，\n",
    "那么我们可以证明$P(\\emptyset) = 0$，即不可能发生事件的概率是$0$。\n",
    "\n",
    "### 随机变量\n",
    "\n",
    "在我们掷骰子的随机实验中，我们引入了*随机变量*（random variable）的概念。\n",
    "随机变量几乎可以是任何数量，并且它可以在随机实验的一组可能性中取一个值。\n",
    "考虑一个随机变量$X$，其值在掷骰子的样本空间$\\mathcal{S}=\\{1,2,3,4,5,6\\}$中。\n",
    "我们可以将事件“看到一个$5$”表示为$\\{X=5\\}$或$X=5$，\n",
    "其概率表示为$P(\\{X=5\\})$或$P(X=5)$。\n",
    "通过$P(X=a)$，我们区分了随机变量$X$和$X$可以采取的值（例如$a$）。\n",
    "然而，这可能会导致繁琐的表示。\n",
    "为了简化符号，一方面，我们可以将$P(X)$表示为随机变量$X$上的*分布*（distribution）：\n",
    "分布告诉我们$X$获得某一值的概率。\n",
    "另一方面，我们可以简单用$P(a)$表示随机变量取值$a$的概率。\n",
    "由于概率论中的事件是来自样本空间的一组结果，因此我们可以为随机变量指定值的可取范围。\n",
    "例如，$P(1 \\leq X \\leq 3)$表示事件$\\{1 \\leq X \\leq 3\\}$，\n",
    "即$\\{X = 1, 2, \\text{or}, 3\\}$的概率。\n",
    "等价地，$P(1 \\leq X \\leq 3)$表示随机变量$X$从$\\{1, 2, 3\\}$中取值的概率。\n",
    "\n",
    "请注意，*离散*（discrete）随机变量（如骰子的每一面）\n",
    "和*连续*（continuous）随机变量（如人的体重和身高）之间存在微妙的区别。\n",
    "现实生活中，测量两个人是否具有完全相同的身高没有太大意义。\n",
    "如果我们进行足够精确的测量，你会发现这个星球上没有两个人具有完全相同的身高。\n",
    "在这种情况下，询问某人的身高是否落入给定的区间，比如是否在1.79米和1.81米之间更有意义。\n",
    "在这些情况下，我们将这个看到某个数值的可能性量化为*密度*（density）。\n",
    "高度恰好为1.80米的概率为0，但密度不是0。\n",
    "在任何两个不同高度之间的区间，我们都有非零的概率。\n",
    "在本节的其余部分中，我们将考虑离散空间中的概率。\n",
    "对于连续随机变量的概率，你可以参考深度学习数学附录中[随机变量](https://d2l.ai/chapter_appendix-mathematics-for-deep-learning/random-variables.html)\n",
    "的一节。\n",
    "\n",
    "## 处理多个随机变量\n",
    "\n",
    "很多时候，我们会考虑多个随机变量。\n",
    "比如，我们可能需要对疾病和症状之间的关系进行建模。\n",
    "给定一个疾病和一个症状，比如“流感”和“咳嗽”，以某个概率存在或不存在于某个患者身上。\n",
    "我们需要估计这些概率以及概率之间的关系，以便我们可以运用我们的推断来实现更好的医疗服务。\n",
    "\n",
    "再举一个更复杂的例子：图像包含数百万像素，因此有数百万个随机变量。\n",
    "在许多情况下，图像会附带一个*标签*（label），标识图像中的对象。\n",
    "我们也可以将标签视为一个随机变量。\n",
    "我们甚至可以将所有元数据视为随机变量，例如位置、时间、光圈、焦距、ISO、对焦距离和相机类型。\n",
    "所有这些都是联合发生的随机变量。\n",
    "当我们处理多个随机变量时，会有若干个变量是我们感兴趣的。\n",
    "\n",
    "### 联合概率\n",
    "\n",
    "第一个被称为*联合概率*（joint probability）$P(A=a,B=b)$。\n",
    "给定任意值$a$和$b$，联合概率可以回答：$A=a$和$B=b$同时满足的概率是多少？\n",
    "请注意，对于任何$a$和$b$的取值，$P(A = a, B=b) \\leq P(A=a)$。\n",
    "这点是确定的，因为要同时发生$A=a$和$B=b$，$A=a$就必须发生，$B=b$也必须发生（反之亦然）。因此，$A=a$和$B=b$同时发生的可能性不大于$A=a$或是$B=b$单独发生的可能性。\n",
    "\n",
    "### 条件概率\n",
    "\n",
    "联合概率的不等式带给我们一个有趣的比率：\n",
    "$0 \\leq \\frac{P(A=a, B=b)}{P(A=a)} \\leq 1$。\n",
    "我们称这个比率为*条件概率*（conditional probability），\n",
    "并用$P(B=b \\mid A=a)$表示它：它是$B=b$的概率，前提是$A=a$已发生。\n",
    "\n",
    "### 贝叶斯定理\n",
    "\n",
    "使用条件概率的定义，我们可以得出统计学中最有用的方程之一：\n",
    "*Bayes定理*（Bayes' theorem）。\n",
    "根据*乘法法则*（multiplication rule ）可得到$P(A, B) = P(B \\mid A) P(A)$。\n",
    "根据对称性，可得到$P(A, B) = P(A \\mid B) P(B)$。\n",
    "假设$P(B)>0$，求解其中一个条件变量，我们得到\n",
    "\n",
    "$$P(A \\mid B) = \\frac{P(B \\mid A) P(A)}{P(B)}.$$\n",
    "\n",
    "请注意，这里我们使用紧凑的表示法：\n",
    "其中$P(A, B)$是一个*联合分布*（joint distribution），\n",
    "$P(A \\mid B)$是一个*条件分布*（conditional distribution）。\n",
    "这种分布可以在给定值$A = a, B=b$上进行求值。\n",
    "\n",
    "### 边际化\n",
    "\n",
    "为了能进行事件概率求和，我们需要*求和法则*（sum rule），\n",
    "即$B$的概率相当于计算$A$的所有可能选择，并将所有选择的联合概率聚合在一起：\n",
    "\n",
    "$$P(B) = \\sum_{A} P(A, B),$$\n",
    "\n",
    "这也称为*边际化*（marginalization）。\n",
    "边际化结果的概率或分布称为*边际概率*（marginal probability）\n",
    "或*边际分布*（marginal distribution）。\n",
    "\n",
    "### 独立性\n",
    "\n",
    "另一个有用属性是*依赖*（dependence）与*独立*（independence）。\n",
    "如果两个随机变量$A$和$B$是独立的，意味着事件$A$的发生跟$B$事件的发生无关。\n",
    "在这种情况下，统计学家通常将这一点表述为$A \\perp  B$。\n",
    "根据贝叶斯定理，马上就能同样得到$P(A \\mid B) = P(A)$。\n",
    "在所有其他情况下，我们称$A$和$B$依赖。\n",
    "比如，两次连续抛出一个骰子的事件是相互独立的。\n",
    "相比之下，灯开关的位置和房间的亮度并不是（因为可能存在灯泡坏掉、电源故障，或者开关故障）。\n",
    "\n",
    "由于$P(A \\mid B) = \\frac{P(A, B)}{P(B)} = P(A)$等价于$P(A, B) = P(A)P(B)$，\n",
    "因此两个随机变量是独立的，当且仅当两个随机变量的联合分布是其各自分布的乘积。\n",
    "同样地，给定另一个随机变量$C$时，两个随机变量$A$和$B$是*条件独立的*（conditionally independent），\n",
    "当且仅当$P(A, B \\mid C) = P(A \\mid C)P(B \\mid C)$。\n",
    "这个情况表示为$A \\perp B \\mid C$。\n",
    "\n",
    "### 应用\n",
    ":label:`subsec_probability_hiv_app`\n",
    "\n",
    "我们实战演练一下！\n",
    "假设一个医生对患者进行艾滋病病毒（HIV）测试。\n",
    "这个测试是相当准确的，如果患者健康但测试显示他患病，这个概率只有1%；\n",
    "如果患者真正感染HIV，它永远不会检测不出。\n",
    "我们使用$D_1$来表示诊断结果（如果阳性，则为$1$，如果阴性，则为$0$），\n",
    "$H$来表示感染艾滋病病毒的状态（如果阳性，则为$1$，如果阴性，则为$0$）。\n",
    "在 :numref:`conditional_prob_D1`中列出了这样的条件概率。\n",
    "\n",
    ":条件概率为$P(D_1 \\mid H)$\n",
    "\n",
    "| 条件概率 | $H=1$ | $H=0$ |\n",
    "|---|---|---|\n",
    "|$P(D_1 = 1 \\mid H)$|            1 |         0.01 |\n",
    "|$P(D_1 = 0 \\mid H)$|            0 |         0.99 |\n",
    ":label:`conditional_prob_D1`\n",
    "\n",
    "请注意，每列的加和都是1（但每行的加和不是），因为条件概率需要总和为1，就像概率一样。\n",
    "让我们计算如果测试出来呈阳性，患者感染HIV的概率，即$P(H = 1 \\mid D_1 = 1)$。\n",
    "显然，这将取决于疾病有多常见，因为它会影响错误警报的数量。\n",
    "假设人口总体是相当健康的，例如，$P(H=1) = 0.0015$。\n",
    "为了应用贝叶斯定理，我们需要运用边际化和乘法法则来确定\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1) \\\\\n",
    "=& P(D_1=1, H=0) + P(D_1=1, H=1)  \\\\\n",
    "=& P(D_1=1 \\mid H=0) P(H=0) + P(D_1=1 \\mid H=1) P(H=1) \\\\\n",
    "=& 0.011485.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "因此，我们得到\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(H = 1 \\mid D_1 = 1)\\\\ =& \\frac{P(D_1=1 \\mid H=1) P(H=1)}{P(D_1=1)} \\\\ =& 0.1306 \\end{aligned}.$$\n",
    "\n",
    "换句话说，尽管使用了非常准确的测试，患者实际上患有艾滋病的几率只有13.06%。\n",
    "正如我们所看到的，概率可能是违反直觉的。\n",
    "\n",
    "患者在收到这样可怕的消息后应该怎么办？\n",
    "很可能，患者会要求医生进行另一次测试来确定病情。\n",
    "第二个测试具有不同的特性，它不如第一个测试那么精确，\n",
    "如 :numref:`conditional_prob_D2`所示。\n",
    "\n",
    ":条件概率为$P(D_2 \\mid H)$\n",
    "\n",
    "| 条件概率 | $H=1$ | $H=0$ |\n",
    "|---|---|---|\n",
    "|$P(D_2 = 1 \\mid H)$|            0.98 |         0.03 |\n",
    "|$P(D_2 = 0 \\mid H)$|            0.02 |         0.97 |\n",
    ":label:`conditional_prob_D2`\n",
    "\n",
    "不幸的是，第二次测试也显示阳性。让我们通过假设条件独立性来计算出应用Bayes定理的必要概率：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1 \\mid H = 0) \\\\\n",
    "=& P(D_1 = 1 \\mid H = 0) P(D_2 = 1 \\mid H = 0)  \\\\\n",
    "=& 0.0003,\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1 \\mid H = 1) \\\\\n",
    "=& P(D_1 = 1 \\mid H = 1) P(D_2 = 1 \\mid H = 1)  \\\\\n",
    "=& 0.98.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "现在我们可以应用边际化和乘法规则：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1) \\\\\n",
    "=& P(D_1 = 1, D_2 = 1, H = 0) + P(D_1 = 1, D_2 = 1, H = 1)  \\\\\n",
    "=& P(D_1 = 1, D_2 = 1 \\mid H = 0)P(H=0) + P(D_1 = 1, D_2 = 1 \\mid H = 1)P(H=1)\\\\\n",
    "=& 0.00176955.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "最后，鉴于存在两次阳性检测，患者患有艾滋病的概率为\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(H = 1 \\mid D_1 = 1, D_2 = 1)\\\\\n",
    "=& \\frac{P(D_1 = 1, D_2 = 1 \\mid H=1) P(H=1)}{P(D_1 = 1, D_2 = 1)} \\\\\n",
    "=& 0.8307.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "也就是说，第二次测试使我们能够对患病的情况获得更高的信心。\n",
    "尽管第二次检验比第一次检验的准确性要低得多，但它仍然显著提高我们的预测概率。\n",
    "\n",
    "## 期望和方差\n",
    "\n",
    "为了概括概率分布的关键特征，我们需要一些测量方法。\n",
    "一个随机变量$X$的*期望*（expectation，或平均值（average））表示为\n",
    "\n",
    "$$E[X] = \\sum_{x} x P(X = x).$$\n",
    "\n",
    "当函数$f(x)$的输入是从分布$P$中抽取的随机变量时，$f(x)$的期望值为\n",
    "\n",
    "$$E_{x \\sim P}[f(x)] = \\sum_x f(x) P(x).$$\n",
    "\n",
    "在许多情况下，我们希望衡量随机变量$X$与其期望值的偏置。这可以通过方差来量化\n",
    "\n",
    "$$\\mathrm{Var}[X] = E\\left[(X - E[X])^2\\right] =\n",
    "E[X^2] - E[X]^2.$$\n",
    "\n",
    "方差的平方根被称为*标准差*（standard deviation）。\n",
    "随机变量函数的方差衡量的是：当从该随机变量分布中采样不同值$x$时，\n",
    "函数值偏离该函数的期望的程度：\n",
    "\n",
    "$$\\mathrm{Var}[f(x)] = E\\left[\\left(f(x) - E[f(x)]\\right)^2\\right].$$\n",
    "\n",
    "## 小结\n",
    "\n",
    "* 我们可以从概率分布中采样。\n",
    "* 我们可以使用联合分布、条件分布、Bayes定理、边缘化和独立性假设来分析多个随机变量。\n",
    "* 期望和方差为概率分布的关键特征的概括提供了实用的度量形式。\n",
    "\n",
    "## 练习\n",
    "\n",
    "1. 进行$m=500$组实验，每组抽取$n=10$个样本。改变$m$和$n$，观察和分析实验结果。\n",
    "2. 给定两个概率为$P(\\mathcal{A})$和$P(\\mathcal{B})$的事件，计算$P(\\mathcal{A} \\cup \\mathcal{B})$和$P(\\mathcal{A} \\cap \\mathcal{B})$的上限和下限。（提示：使用[友元图](https://en.wikipedia.org/wiki/Venn_diagram)来展示这些情况。)\n",
    "3. 假设我们有一系列随机变量，例如$A$、$B$和$C$，其中$B$只依赖于$A$，而$C$只依赖于$B$，你能简化联合概率$P(A, B, C)$吗？（提示：这是一个[马尔可夫链](https://en.wikipedia.org/wiki/Markov_chain)。)\n",
    "4. 在 :numref:`subsec_probability_hiv_app`中，第一个测试更准确。为什么不运行第一个测试两次，而是同时运行第一个和第二个测试?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 22,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "[Discussions](https://discuss.d2l.ai/t/1762)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}